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Papers by Enrico Mazziotti

Research paper thumbnail of Existence and uniqueness results for a class of non linear models

arXiv (Cornell University), Mar 11, 2012

The qualitative analysis of the initial value problem P related to a non linear third order parab... more The qualitative analysis of the initial value problem P related to a non linear third order parabolic equation typical of diffusive models is discussed. Some basic properties of the the fundamental solution of a related linear operator are determined and are applied to an equivalent integro differential formulation of the problem. By the fixed point theorem, existence and uniqueness results are obtained.

Research paper thumbnail of Sulla propagazione ondosa in un sistema viscoelastico lineare in presenza di forze di massa

Annali Dell'universita' Di Ferrara, 1979

Riassunto Si studia la propagazione ondosa che si determina in un sistema viscoelastico lineare ... more Riassunto Si studia la propagazione ondosa che si determina in un sistema viscoelastico lineare sotto l'azione di assegnate forze di massa e per effetto di prefissate condizioni al contorno. Mediante l'analisi asintotica di una particolare serie di Neumann che interviene nella soluzione, si dimostrapoi l'esistenza di una regione di «strato limite» pert→∞, in corrispondenza di tempi di rilassamento molto «piccoli».

Research paper thumbnail of Wave progation in a linear viscoelatic system in the presence of mass forces

Research paper thumbnail of Fenomeni di propagazione e diffusione in superconduttivita

l 101 Convegno Nazionale AEIT, 2007

Research paper thumbnail of Existence and uniqueness results for a class of nonlinear differential systems with second-order differences

PAMM, 2008

In a real Hilbert space we investigate the existence, uniqueness and asymptotic properties of the... more In a real Hilbert space we investigate the existence, uniqueness and asymptotic properties of the strong and weak solutions to an infinite nonlinear differential system with second-order differences, subject to an extreme condition and initial data.

Research paper thumbnail of Non linear travelling waves with diffusion

arXiv: Mathematical Physics, 2012

A third order parabolic operator L_\epsilon typical of a non linear wave operator cal L_0 perturb... more A third order parabolic operator L_\epsilon typical of a non linear wave operator cal L_0 perturbed by viscous terms, is analyzed. Some particular solutions related to L_0 are explicitly determined and the initial value problem for L_\epsilon is considered. The parabolic-hyperbolic behaviour is analyzed and rigorous approximations of the solution are achieved.

Research paper thumbnail of Conseguenze fisiche e geometriche dell'uso di riferimenti fisici comobili nel caso di scelta di coordinate isotrope

Relatività generale e fisica della gravitazione, 1986

Research paper thumbnail of On kinks and other travelling-wave solutions of a modified sine-Gordon equation

Meccanica, 2015

We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a pe... more We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. On the real line candidate orbitally stable solutions with bounded energy density are either the constant one, or of kink (i.e. soliton) type, or of array-of-kinks type, or of "half-array-of-kinks" type. While the first three have unperturbed analogs, the last type is essentially new. We also propose a convergent method of successive approximations of the (anti)kink solution based on a careful application of the fixed point theorem.

Research paper thumbnail of Sull’unicita della soluzione delle equazioni della dinamica dei corpi viscoelastici in un dominio illimitato

Research paper thumbnail of Reference frames in harmonic coordinates: geometric and physical aspects

Ricerche di Matematica, 2012

This work is focused on the geometrical and physical characteristics of the class of reference fr... more This work is focused on the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates. Precisely, we express in relative form the harmonicity conditions and consider the so called "spatially harmonicity" of a reference frame in spherical symmetry. The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions.

Research paper thumbnail of Reference frames in harmonic coordinates: geometric and physical aspects

Ricerche di Matematica, 2012

This work is focused on the geometrical and physical characteristics of the class of reference fr... more This work is focused on the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates. Precisely, we express in relative form the harmonicity conditions and consider the so called "spatially harmonicity" of a reference frame in spherical symmetry. The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions.

Research paper thumbnail of On geometrical and physical consequences of using certain special classes of comoving physical frames of reference

Journal of Interdisciplinary Mathematics, 2009

This paper derrelops the studv of the geometrical characteristics of the class of frames of refer... more This paper derrelops the studv of the geometrical characteristics of the class of frames of reference associated rvith the tr.r'o u'ell known sets of coorclinates: Levi-Civita's curvature coclrdinates and ganssian polar coordinates. In particular, thr:ough the separate invariant forrnulation of the rrritial clata problem ancl oi the restricted errolntion problem, the analysis is applierl to a sphericallr, syrnmetric perfect flr-rid, r,r'hose stream lines coincide r,r'ith those of the above rnentiorrecl class of frames.

Research paper thumbnail of On geometrical and physical consequences of using certain special classes of comoving physical frames of reference II

Journal of Interdisciplinary Mathematics, 2011

Research paper thumbnail of Existence and uniqueness results for a class of non linear models

arXiv (Cornell University), Mar 11, 2012

The qualitative analysis of the initial value problem P related to a non linear third order parab... more The qualitative analysis of the initial value problem P related to a non linear third order parabolic equation typical of diffusive models is discussed. Some basic properties of the the fundamental solution of a related linear operator are determined and are applied to an equivalent integro differential formulation of the problem. By the fixed point theorem, existence and uniqueness results are obtained.

Research paper thumbnail of Sulla propagazione ondosa in un sistema viscoelastico lineare in presenza di forze di massa

Annali Dell'universita' Di Ferrara, 1979

Riassunto Si studia la propagazione ondosa che si determina in un sistema viscoelastico lineare ... more Riassunto Si studia la propagazione ondosa che si determina in un sistema viscoelastico lineare sotto l'azione di assegnate forze di massa e per effetto di prefissate condizioni al contorno. Mediante l'analisi asintotica di una particolare serie di Neumann che interviene nella soluzione, si dimostrapoi l'esistenza di una regione di «strato limite» pert→∞, in corrispondenza di tempi di rilassamento molto «piccoli».

Research paper thumbnail of Wave progation in a linear viscoelatic system in the presence of mass forces

Research paper thumbnail of Fenomeni di propagazione e diffusione in superconduttivita

l 101 Convegno Nazionale AEIT, 2007

Research paper thumbnail of Existence and uniqueness results for a class of nonlinear differential systems with second-order differences

PAMM, 2008

In a real Hilbert space we investigate the existence, uniqueness and asymptotic properties of the... more In a real Hilbert space we investigate the existence, uniqueness and asymptotic properties of the strong and weak solutions to an infinite nonlinear differential system with second-order differences, subject to an extreme condition and initial data.

Research paper thumbnail of Non linear travelling waves with diffusion

arXiv: Mathematical Physics, 2012

A third order parabolic operator L_\epsilon typical of a non linear wave operator cal L_0 perturb... more A third order parabolic operator L_\epsilon typical of a non linear wave operator cal L_0 perturbed by viscous terms, is analyzed. Some particular solutions related to L_0 are explicitly determined and the initial value problem for L_\epsilon is considered. The parabolic-hyperbolic behaviour is analyzed and rigorous approximations of the solution are achieved.

Research paper thumbnail of Conseguenze fisiche e geometriche dell'uso di riferimenti fisici comobili nel caso di scelta di coordinate isotrope

Relatività generale e fisica della gravitazione, 1986

Research paper thumbnail of On kinks and other travelling-wave solutions of a modified sine-Gordon equation

Meccanica, 2015

We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a pe... more We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. On the real line candidate orbitally stable solutions with bounded energy density are either the constant one, or of kink (i.e. soliton) type, or of array-of-kinks type, or of "half-array-of-kinks" type. While the first three have unperturbed analogs, the last type is essentially new. We also propose a convergent method of successive approximations of the (anti)kink solution based on a careful application of the fixed point theorem.

Research paper thumbnail of Sull’unicita della soluzione delle equazioni della dinamica dei corpi viscoelastici in un dominio illimitato

Research paper thumbnail of Reference frames in harmonic coordinates: geometric and physical aspects

Ricerche di Matematica, 2012

This work is focused on the geometrical and physical characteristics of the class of reference fr... more This work is focused on the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates. Precisely, we express in relative form the harmonicity conditions and consider the so called "spatially harmonicity" of a reference frame in spherical symmetry. The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions.

Research paper thumbnail of Reference frames in harmonic coordinates: geometric and physical aspects

Ricerche di Matematica, 2012

This work is focused on the geometrical and physical characteristics of the class of reference fr... more This work is focused on the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates. Precisely, we express in relative form the harmonicity conditions and consider the so called "spatially harmonicity" of a reference frame in spherical symmetry. The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions.

Research paper thumbnail of On geometrical and physical consequences of using certain special classes of comoving physical frames of reference

Journal of Interdisciplinary Mathematics, 2009

This paper derrelops the studv of the geometrical characteristics of the class of frames of refer... more This paper derrelops the studv of the geometrical characteristics of the class of frames of reference associated rvith the tr.r'o u'ell known sets of coorclinates: Levi-Civita's curvature coclrdinates and ganssian polar coordinates. In particular, thr:ough the separate invariant forrnulation of the rrritial clata problem ancl oi the restricted errolntion problem, the analysis is applierl to a sphericallr, syrnmetric perfect flr-rid, r,r'hose stream lines coincide r,r'ith those of the above rnentiorrecl class of frames.

Research paper thumbnail of On geometrical and physical consequences of using certain special classes of comoving physical frames of reference II

Journal of Interdisciplinary Mathematics, 2011