Georgi Boyadzhiev - Profile on Academia.edu (original) (raw)

Papers by Georgi Boyadzhiev

Viscosity solutions and strong maximum principle for weakly coupled cooperative parabolic systems with nonlinear principle part

THE 5TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE IN INFORMATION SYSTEMS (CIIS 2022): Intelligent and Resilient Digital Innovations for Sustainable Living

Dynamics of Modified Lotka–Volterra Model with Polynomial Intervention Factors. Methodological Aspects. III

International journal of differential equations and applications, Oct 15, 2021

Операторы рекурсии и иерархии модифицированных уравнений Кортевега-де Фриза, связанные с алгебрами Каца-Муди D4(1)D_4^{(1)}D4(1), D4(2)D_4^{(2)}D4(2) и D4(3)D_4^{(3)}D4(3)

Teoreticheskaya i Matematicheskaya Fizika, 2020

Построены три неэквивалентные градуировки алгебры D4simeqso(8)D_4 \simeq so(8)D4simeqso(8). Первая градуировка стандарт... more Построены три неэквивалентные градуировки алгебры D4simeqso(8)D_4 \simeq so(8)D4simeqso(8). Первая градуировка стандартна, она получается с помощью автоморфизма Коксетера C1=Salpha2Salpha1Salpha3Salpha4C_1=S_{\alpha_2} S_{\alpha_1}S_{\alpha_3}S_{\alpha_4}C1=Salpha2Salpha1Salpha3Salpha4 из ее диэдрального представления, во второй используется C2=C1RC_2 = C_1RC2=C1R, где RRR - зеркальный автоморфизм, в третьей - C3=Salpha2Salpha1TC_3 = S_{\alpha_2}S_{\alpha_1}TC3=Salpha2Salpha1T, где TTT - внешний автоморфизм порядка 3. Для каждой градуировки построены базис в соответствующих линейных подпространствах mathfrakg(k)\mathfrak{g}^{(k)}mathfrakg(k), орбиты автоморфизмов Коксетера и соответствующие пары Лакса, порожденные соответствующими иерархиями модифицированных уравнений Кортевега-де Фриза (мКдФ). Найдены компактные выражения для каждой иерархии в терминах операторов рекурсии. Явно выписаны первые нетривиальные уравнения мКдФ и их гамильтонианы. В действительности для D4(1)D_4^{(1)}D4(1) имеются две системы мКдФ, так как в этом случае показатель 333 имеет кратность 2. Каждая из этих систем мКдФ состоит из четырех уравнений третьего порядк...

Geofizicheskiy Zhurnal, 2022

The task of the work was geoelectrical studies using variations of the magnetotelluric (MT) field... more The task of the work was geoelectrical studies using variations of the magnetotelluric (MT) field of the Kozloduy nuclear power plant (KNPP) region and the integration of its results with other geological and geophysical knowledge. This paper presents the determined interpretation parameters of the MT field. The KNPP is located on the right bank of the Danube River in close proximity to the river. This fact, together with the location of electrified railways determined the unique network of locations of observation points for MT field variations. Based on the analysis of Earthquake Catalogs of Bulgaria and international seismicity databases, a map of the seismicity of nuclear power plant areas was built. Over the past 50 years, about 750 earthquakes (mainly south of KNPP) have been recorded at a distance of 40—80 km from the KNPP. Two magnetotelluric stations GEOMAG-02 were used at measurement sites, but equipment for recording electrical channels was available only for one station ...

Geoelectric Studies of the Kozloduy Nuclear Power Plant Region (Programm KOZLODUY)

11th Congress of the Balkan Geophysical Society, 2021

Journal of Pseudo-Differential Operators and Applications, 2016

Method of sub-and super-solutions is applied in investigation of solvability in classical C 2 (Ω)... more Method of sub-and super-solutions is applied in investigation of solvability in classical C 2 (Ω) C(Ω) sense of quasi-linear non-cooperative weakly coupled systems of elliptic second-order PDE.

Proceedings of the Bulgarian Academy of Sciences

In this paper we study the impact of the hidden cases of Covid-19 spread in Bulgaria by means of ... more In this paper we study the impact of the hidden cases of Covid-19 spread in Bulgaria by means of the SEIR model, in the period December 15, 2021 – until March 2022. In particular, the numerical experiments based on the hidden cases till mid-January, provide a forecast of the peak of the infectious curve about February 8, 2022, and reaching the maximum of about 90 000 cases. The forecast shows that end of the epidemics (in Bulgaria) would be in mid-May, 2022. This forecast is compared to the previous forecasts based on the same data excluding hidden cases; they have shown that the peak will be about February 28, reaching about 75 000 cases and will vanish until end of May. As seen in Fig. 3, our forecast of the end of the particular wave of epidemics shows just two weeks difference with what happened in real life – the wave ended in the first week of June. It is curious, that though the peak of the curve in thehidden cases approach has shifted to February 8, the cumulative number of ...

Proceedings of the Bulgarian Academy of Sciences

We provide a study of the Covid-19 spread in Bulgaria in the period starting December 15, 2021 un... more We provide a study of the Covid-19 spread in Bulgaria in the period starting December 15, 2021 until early February, 2022. In particular, we provide predictive scenarios for the peak of the pandemic. Based on these scenarios, we estimate the risks in terms of fatalities in the case no restrictive measures are imposed. The main challenge is distinguishing the influence of the Delta variant which is still dominating in December, 2021, while Omicron becomes dominant in early January, 2022.

The study presents the results of geoelectric research for seismic risk assessment on the example... more The study presents the results of geoelectric research for seismic risk assessment on the example of the Kozlodui nuclear power plant in Bulgaria. The image of the geoelectric structure in the study area was obtained using one-dimensional inverse electrical resistivity modeling of the full five-component magnetotelluric data and quasi-three-dimensional inverse conductivity modeling of the geomagnetic responses recorded during the summer 2021 field campaign. According to the presented results, the geoelectrically anomalous structure is divided into two levels. The near-surface anomalous structure in the immediate reach of human geotechnical activity corresponds to the electrically conductive sedimentary fill. The mid-crustal layer is coincident with the low seismic velocity zone at the brittle and ductile crust interface, revealed in previous studies. The presented results imply that the geological environment is not affected by large faults capable of transmitting seismic energy fro...

In this paper is given a new approach to 3D medelling of elastic piecewise homogeneous media, in ... more In this paper is given a new approach to 3D medelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on the principle of tomography with Earthquake as a source of the signal and at least three receiver stations on the surface. The wave propagation in such media is described by a system of three strongly coupled hyperbolic equations with piece-wise constant coefitients. The characteristic set and bi-characteristic curves are computed in a homogeneous half-space with free boundary as well as the formulae of reflection and diffraction of the bi-characteristics on the internal boundaries of the media. Applications of the characteristic set and bi-characteristic curves for the inverse problem in geophysics and Earth modelling are given.

In this paper the geometrical properties of the bi-characteristic curves are employed in developi... more In this paper the geometrical properties of the bi-characteristic curves are employed in developing a new approach to 3D modelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on tomography and the refraction, respectively, reflection, of the bi-characteristic curves at the layer boundaries of multi -layered media.

Strong Interior and Boundary Maximum Principle for Weakly Coupled Linear Cooperative Elliptic Systems

Mathematics

In this paper, we consider the validity of the strong maximum principle for weakly coupled, degen... more In this paper, we consider the validity of the strong maximum principle for weakly coupled, degenerate and cooperative elliptic systems in a bounded domain. In particular, we are interested in the viscosity solutions of elliptic systems with fully nonlinear degenerated principal symbol. Applying the method of viscosity solutions, introduced by Crandall, Ishii and Lions in 1992, we prove the validity of strong interior and boundary maximum principle for semi-continuous viscosity sub- and super-solutions of such nonlinear systems. For the first time in the literature, the strong maximum principle is considered for viscosity solutions to nonlinear elliptic systems. As a consequence of the strong interior maximum principle, we derive comparison principle for viscosity sub- and super-solutions in case when on of them is a classical one. The main novelty of this work is the reduction of the smoothness of the solution. In the literature the strong maximum principle is proved for classical ...

RENEWABLE ENERGY SOURCES AND TECHNOLOGIES

One of the most important applications of comparison principle is the well known method of sub-an... more One of the most important applications of comparison principle is the well known method of sub-and super-solutions, known as method of upper-and lower solutions as well. In this paper it is applied to the diffraction problem in bounded domain for cooperative system of quasi-linear parabolic PDE. The existence of upper and lower solutions is shown as well on a model example-reaction diffusion system arising in chemistry. w t − θ(x)w xx − c 2 v v+K 2 θ(x − a) = 0

Strong maximum principle for nonlinear cooperative elliptic systems

RENEWABLE ENERGY SOURCES AND TECHNOLOGIES

This paper presents some sufficient conditions for the validity of the comparison principle for t... more This paper presents some sufficient conditions for the validity of the comparison principle for the weak solutions of non - cooperative weakly coupled systems of elliptic second-order PDEs.

Existence theorem for cooperative quasi-linear elliptic systems

Comptes rendus de l'Académie bulgare des sciences: sciences mathématiques et naturelles

ABSTRACT

Nonlinear Analysis: Theory, Methods & Applications, 2008

Optimization for non-linear inverse problems

RENDICONTI LINCEI, 2008

The non-linear inversion of geophysical data in general does not yield a unique solution, but a s... more The non-linear inversion of geophysical data in general does not yield a unique solution, but a single model representing the investigated field, and is preferred for an easy geological interpretation of observations. The analyzed region is constituted by a number of sub-regions where multi-valued non-linear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the

Viscosity solutions and strong maximum principle for weakly coupled cooperative parabolic systems with nonlinear principle part

THE 5TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE IN INFORMATION SYSTEMS (CIIS 2022): Intelligent and Resilient Digital Innovations for Sustainable Living

Dynamics of Modified Lotka–Volterra Model with Polynomial Intervention Factors. Methodological Aspects. III

International journal of differential equations and applications, Oct 15, 2021

Операторы рекурсии и иерархии модифицированных уравнений Кортевега-де Фриза, связанные с алгебрами Каца-Муди D4(1)D_4^{(1)}D4(1), D4(2)D_4^{(2)}D4(2) и D4(3)D_4^{(3)}D4(3)

Teoreticheskaya i Matematicheskaya Fizika, 2020

Построены три неэквивалентные градуировки алгебры D4simeqso(8)D_4 \simeq so(8)D4simeqso(8). Первая градуировка стандарт... more Построены три неэквивалентные градуировки алгебры D4simeqso(8)D_4 \simeq so(8)D4simeqso(8). Первая градуировка стандартна, она получается с помощью автоморфизма Коксетера C1=Salpha2Salpha1Salpha3Salpha4C_1=S_{\alpha_2} S_{\alpha_1}S_{\alpha_3}S_{\alpha_4}C1=Salpha2Salpha1Salpha3Salpha4 из ее диэдрального представления, во второй используется C2=C1RC_2 = C_1RC2=C1R, где RRR - зеркальный автоморфизм, в третьей - C3=Salpha2Salpha1TC_3 = S_{\alpha_2}S_{\alpha_1}TC3=Salpha2Salpha1T, где TTT - внешний автоморфизм порядка 3. Для каждой градуировки построены базис в соответствующих линейных подпространствах mathfrakg(k)\mathfrak{g}^{(k)}mathfrakg(k), орбиты автоморфизмов Коксетера и соответствующие пары Лакса, порожденные соответствующими иерархиями модифицированных уравнений Кортевега-де Фриза (мКдФ). Найдены компактные выражения для каждой иерархии в терминах операторов рекурсии. Явно выписаны первые нетривиальные уравнения мКдФ и их гамильтонианы. В действительности для D4(1)D_4^{(1)}D4(1) имеются две системы мКдФ, так как в этом случае показатель 333 имеет кратность 2. Каждая из этих систем мКдФ состоит из четырех уравнений третьего порядк...

Geofizicheskiy Zhurnal, 2022

The task of the work was geoelectrical studies using variations of the magnetotelluric (MT) field... more The task of the work was geoelectrical studies using variations of the magnetotelluric (MT) field of the Kozloduy nuclear power plant (KNPP) region and the integration of its results with other geological and geophysical knowledge. This paper presents the determined interpretation parameters of the MT field. The KNPP is located on the right bank of the Danube River in close proximity to the river. This fact, together with the location of electrified railways determined the unique network of locations of observation points for MT field variations. Based on the analysis of Earthquake Catalogs of Bulgaria and international seismicity databases, a map of the seismicity of nuclear power plant areas was built. Over the past 50 years, about 750 earthquakes (mainly south of KNPP) have been recorded at a distance of 40—80 km from the KNPP. Two magnetotelluric stations GEOMAG-02 were used at measurement sites, but equipment for recording electrical channels was available only for one station ...

Geoelectric Studies of the Kozloduy Nuclear Power Plant Region (Programm KOZLODUY)

11th Congress of the Balkan Geophysical Society, 2021

Journal of Pseudo-Differential Operators and Applications, 2016

Method of sub-and super-solutions is applied in investigation of solvability in classical C 2 (Ω)... more Method of sub-and super-solutions is applied in investigation of solvability in classical C 2 (Ω) C(Ω) sense of quasi-linear non-cooperative weakly coupled systems of elliptic second-order PDE.

Proceedings of the Bulgarian Academy of Sciences

In this paper we study the impact of the hidden cases of Covid-19 spread in Bulgaria by means of ... more In this paper we study the impact of the hidden cases of Covid-19 spread in Bulgaria by means of the SEIR model, in the period December 15, 2021 – until March 2022. In particular, the numerical experiments based on the hidden cases till mid-January, provide a forecast of the peak of the infectious curve about February 8, 2022, and reaching the maximum of about 90 000 cases. The forecast shows that end of the epidemics (in Bulgaria) would be in mid-May, 2022. This forecast is compared to the previous forecasts based on the same data excluding hidden cases; they have shown that the peak will be about February 28, reaching about 75 000 cases and will vanish until end of May. As seen in Fig. 3, our forecast of the end of the particular wave of epidemics shows just two weeks difference with what happened in real life – the wave ended in the first week of June. It is curious, that though the peak of the curve in thehidden cases approach has shifted to February 8, the cumulative number of ...

Proceedings of the Bulgarian Academy of Sciences

We provide a study of the Covid-19 spread in Bulgaria in the period starting December 15, 2021 un... more We provide a study of the Covid-19 spread in Bulgaria in the period starting December 15, 2021 until early February, 2022. In particular, we provide predictive scenarios for the peak of the pandemic. Based on these scenarios, we estimate the risks in terms of fatalities in the case no restrictive measures are imposed. The main challenge is distinguishing the influence of the Delta variant which is still dominating in December, 2021, while Omicron becomes dominant in early January, 2022.

The study presents the results of geoelectric research for seismic risk assessment on the example... more The study presents the results of geoelectric research for seismic risk assessment on the example of the Kozlodui nuclear power plant in Bulgaria. The image of the geoelectric structure in the study area was obtained using one-dimensional inverse electrical resistivity modeling of the full five-component magnetotelluric data and quasi-three-dimensional inverse conductivity modeling of the geomagnetic responses recorded during the summer 2021 field campaign. According to the presented results, the geoelectrically anomalous structure is divided into two levels. The near-surface anomalous structure in the immediate reach of human geotechnical activity corresponds to the electrically conductive sedimentary fill. The mid-crustal layer is coincident with the low seismic velocity zone at the brittle and ductile crust interface, revealed in previous studies. The presented results imply that the geological environment is not affected by large faults capable of transmitting seismic energy fro...

In this paper is given a new approach to 3D medelling of elastic piecewise homogeneous media, in ... more In this paper is given a new approach to 3D medelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on the principle of tomography with Earthquake as a source of the signal and at least three receiver stations on the surface. The wave propagation in such media is described by a system of three strongly coupled hyperbolic equations with piece-wise constant coefitients. The characteristic set and bi-characteristic curves are computed in a homogeneous half-space with free boundary as well as the formulae of reflection and diffraction of the bi-characteristics on the internal boundaries of the media. Applications of the characteristic set and bi-characteristic curves for the inverse problem in geophysics and Earth modelling are given.

In this paper the geometrical properties of the bi-characteristic curves are employed in developi... more In this paper the geometrical properties of the bi-characteristic curves are employed in developing a new approach to 3D modelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on tomography and the refraction, respectively, reflection, of the bi-characteristic curves at the layer boundaries of multi -layered media.

Strong Interior and Boundary Maximum Principle for Weakly Coupled Linear Cooperative Elliptic Systems

Mathematics

In this paper, we consider the validity of the strong maximum principle for weakly coupled, degen... more In this paper, we consider the validity of the strong maximum principle for weakly coupled, degenerate and cooperative elliptic systems in a bounded domain. In particular, we are interested in the viscosity solutions of elliptic systems with fully nonlinear degenerated principal symbol. Applying the method of viscosity solutions, introduced by Crandall, Ishii and Lions in 1992, we prove the validity of strong interior and boundary maximum principle for semi-continuous viscosity sub- and super-solutions of such nonlinear systems. For the first time in the literature, the strong maximum principle is considered for viscosity solutions to nonlinear elliptic systems. As a consequence of the strong interior maximum principle, we derive comparison principle for viscosity sub- and super-solutions in case when on of them is a classical one. The main novelty of this work is the reduction of the smoothness of the solution. In the literature the strong maximum principle is proved for classical ...

RENEWABLE ENERGY SOURCES AND TECHNOLOGIES

One of the most important applications of comparison principle is the well known method of sub-an... more One of the most important applications of comparison principle is the well known method of sub-and super-solutions, known as method of upper-and lower solutions as well. In this paper it is applied to the diffraction problem in bounded domain for cooperative system of quasi-linear parabolic PDE. The existence of upper and lower solutions is shown as well on a model example-reaction diffusion system arising in chemistry. w t − θ(x)w xx − c 2 v v+K 2 θ(x − a) = 0

Strong maximum principle for nonlinear cooperative elliptic systems

RENEWABLE ENERGY SOURCES AND TECHNOLOGIES

This paper presents some sufficient conditions for the validity of the comparison principle for t... more This paper presents some sufficient conditions for the validity of the comparison principle for the weak solutions of non - cooperative weakly coupled systems of elliptic second-order PDEs.

Existence theorem for cooperative quasi-linear elliptic systems

Comptes rendus de l'Académie bulgare des sciences: sciences mathématiques et naturelles

ABSTRACT

Nonlinear Analysis: Theory, Methods & Applications, 2008

Optimization for non-linear inverse problems

RENDICONTI LINCEI, 2008

The non-linear inversion of geophysical data in general does not yield a unique solution, but a s... more The non-linear inversion of geophysical data in general does not yield a unique solution, but a single model representing the investigated field, and is preferred for an easy geological interpretation of observations. The analyzed region is constituted by a number of sub-regions where multi-valued non-linear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the