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Papers by Irena Lasiecka

Research paper thumbnail of Supplement to Numerical Approximations of Algebraic Riccati Equations for Abstract Systems Modelled by Analytic Semigroups, and Applications

Mathematics of Computation, 1991

Research paper thumbnail of Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions

This paper studies a wave equation on a bounded domain in with nonlinear dissipation which is loc... more This paper studies a wave equation on a bounded domain in with nonlinear dissipation which is localized on a subset of the boundary. The damping is modeled by a continuous monotone function without the usual growth restrictions imposed at the origin and infinity. Under the assumption that the observability inequality is satisfied by the solution of the associated linear problem, the asymptotic decay rates of the energy functional are obtained by reducing the nonlinear PDE problem to a linear PDE and a nonlinear ODE. This approach offers a generalized framework which incorporates the results on energy decay that appeared previously in the literature; the method accommodates systems with variable coefficients in the principal elliptic part, and allows to dispense with linear restrictions on the growth of the dissipative feedback map.

Research paper thumbnail of Sensitivity Analysis of Optimal Control Problems for Wave Equations

Siam J Contr Optimizat, 1991

Research paper thumbnail of Exact controllability and uniform stabilization of Kircho plates with boundary control only on

Research paper thumbnail of State constrained control problems for parabolic systems: Regularity of optimal solutions

Appl Math Opt, 1980

Quadratic control problems for parabolic equations withstate constraints are considered. Regulari... more Quadratic control problems for parabolic equations withstate constraints are considered. Regularity (smoothness) of the optimal solution is investigated. It is shown that the optimal control is continuous in time with the values inL2(O) and its time derivative belongs toL2[OT×O].

Research paper thumbnail of Convergence Estimates for Semidiscrete Approximations of Nonselfadjoint Parabolic Equations

Siam J Numer Anal, 1984

... i(A)= {fEL2(r IAfEL2(f);fIr=Oor (af-) o 0} where af/an stands for the normal derivative. It i... more ... i(A)= {fEL2(r IAfEL2(f);fIr=Oor (af-) o 0} where af/an stands for the normal derivative. It is a well-known fact that -A generates on L2(fl) a strongly continuous, analytic semigroup S(t) = eAt such that (2.1) IS (t)l C e wt. ... Page 3. 896 IRENA LASIECKA (see [P1]) ...

Research paper thumbnail of An Observability Estimate in L

Research paper thumbnail of Finite rank, relatively bounded perturbations of semigroups generators. II: Spectrum and Riesz basis assignment with applications to feedback systems

Annali Di Matematica Pura Ed Applicata, 1986

Research paper thumbnail of Local exponential stabilization for a nonlinearly perturbed von Kármán plate

Nonlinear Analysis Theory Methods Applications, Feb 29, 1992

Research paper thumbnail of Sharp Regularity of the Second Time Derivative w_t T of Solutions to Kirchhoff Equations With Clamped Boundary Conditions

International Journal of Applied Mathematics and Computer Science, 2001

Research paper thumbnail of Moore–Gibson–Thompson equation with memory, part II: General decay of energy

Journal of Differential Equations, 2015

Research paper thumbnail of Applied Mathematics and Optimization, vol. 55 n. 2 Marzo/Aprile 2007

Research paper thumbnail of Continuous finite elements in space and time for the nonhomogeneous wave equation

Computers Mathematics With Applications, Feb 28, 1994

Research paper thumbnail of Optimal convergence rates for semidiscrete approximations of parabolic problems with nonsmooth boundary data

Http Dx Doi Org 10 1080 01630569108816443, May 15, 2007

ABSTRACT

Research paper thumbnail of Exponential decay for low and higher energies in the third order linear Moore-Gibson-Thompson equation with variable viscosity

ABSTRACT We consider the Moore-Gibson-Thompson equation which arises, e.g., as a linearization of... more ABSTRACT We consider the Moore-Gibson-Thompson equation which arises, e.g., as a linearization of a model for wave propagation in viscous thermally relaxing fluids. This third order in time equation displays, even in the linear version, a variety of dynamical behaviors for their solutions that depend on the physical parameters in the equation. These range from non-existence and instability to exponential stability (in time). By neglecting diffusivity of the sound coefficient there is a lack of generation of a semigroup associated with the linear dynamics. When diffusivity of the sound is positive, the linear dynamics is described by a strongly continuous evolution. We shall show that this evolution is exponentially stable provided sufficiently large viscous damping is accounted for in the model. The viscosity considered is time and space dependent which then leads to evolution rather then semigroup generators. Decay rates for both natural and higher level energies are derived.

Research paper thumbnail of Algebraic riccati equations with unbounded input → solution operator: applications to boundary control for wave and plate problems

Research paper thumbnail of Boundary control of parabolic systems: Regularity of optimal solutions

Appl Math Opt, 1977

... Irena Lasiecka Department of System Science, University of California at Los Angeles, Los Ang... more ... Irena Lasiecka Department of System Science, University of California at Los Angeles, Los Angeles, California ... coefficients in 9. Since T is assumed to be strongly elliptic, then there exists a constant a >0 such that the quadratic form N X aij~i~j > ot X ~i 2 for all ¢ E fL i=l i=l ...

Research paper thumbnail of Regularity and Strong Convergence of a Variational Approximation to a Nonhomogeneous Dirichlet Hyperbolic Boundary Value Problem

Siam Journal on Mathematical Analysis, Jul 17, 2006

Research paper thumbnail of Exponential local stability of first order strictly hyperbolic systems with nonlinear perturbations on the boundary

Lecture Notes in Control and Information Sciences, 1988

Research paper thumbnail of Exponential stabilization, via Riccati operator, of hyperbolic systems with uncontrolled, unbounded perturbations

Research paper thumbnail of Supplement to Numerical Approximations of Algebraic Riccati Equations for Abstract Systems Modelled by Analytic Semigroups, and Applications

Mathematics of Computation, 1991

Research paper thumbnail of Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions

This paper studies a wave equation on a bounded domain in with nonlinear dissipation which is loc... more This paper studies a wave equation on a bounded domain in with nonlinear dissipation which is localized on a subset of the boundary. The damping is modeled by a continuous monotone function without the usual growth restrictions imposed at the origin and infinity. Under the assumption that the observability inequality is satisfied by the solution of the associated linear problem, the asymptotic decay rates of the energy functional are obtained by reducing the nonlinear PDE problem to a linear PDE and a nonlinear ODE. This approach offers a generalized framework which incorporates the results on energy decay that appeared previously in the literature; the method accommodates systems with variable coefficients in the principal elliptic part, and allows to dispense with linear restrictions on the growth of the dissipative feedback map.

Research paper thumbnail of Sensitivity Analysis of Optimal Control Problems for Wave Equations

Siam J Contr Optimizat, 1991

Research paper thumbnail of Exact controllability and uniform stabilization of Kircho plates with boundary control only on

Research paper thumbnail of State constrained control problems for parabolic systems: Regularity of optimal solutions

Appl Math Opt, 1980

Quadratic control problems for parabolic equations withstate constraints are considered. Regulari... more Quadratic control problems for parabolic equations withstate constraints are considered. Regularity (smoothness) of the optimal solution is investigated. It is shown that the optimal control is continuous in time with the values inL2(O) and its time derivative belongs toL2[OT×O].

Research paper thumbnail of Convergence Estimates for Semidiscrete Approximations of Nonselfadjoint Parabolic Equations

Siam J Numer Anal, 1984

... i(A)= {fEL2(r IAfEL2(f);fIr=Oor (af-) o 0} where af/an stands for the normal derivative. It i... more ... i(A)= {fEL2(r IAfEL2(f);fIr=Oor (af-) o 0} where af/an stands for the normal derivative. It is a well-known fact that -A generates on L2(fl) a strongly continuous, analytic semigroup S(t) = eAt such that (2.1) IS (t)l C e wt. ... Page 3. 896 IRENA LASIECKA (see [P1]) ...

Research paper thumbnail of An Observability Estimate in L

Research paper thumbnail of Finite rank, relatively bounded perturbations of semigroups generators. II: Spectrum and Riesz basis assignment with applications to feedback systems

Annali Di Matematica Pura Ed Applicata, 1986

Research paper thumbnail of Local exponential stabilization for a nonlinearly perturbed von Kármán plate

Nonlinear Analysis Theory Methods Applications, Feb 29, 1992

Research paper thumbnail of Sharp Regularity of the Second Time Derivative w_t T of Solutions to Kirchhoff Equations With Clamped Boundary Conditions

International Journal of Applied Mathematics and Computer Science, 2001

Research paper thumbnail of Moore–Gibson–Thompson equation with memory, part II: General decay of energy

Journal of Differential Equations, 2015

Research paper thumbnail of Applied Mathematics and Optimization, vol. 55 n. 2 Marzo/Aprile 2007

Research paper thumbnail of Continuous finite elements in space and time for the nonhomogeneous wave equation

Computers Mathematics With Applications, Feb 28, 1994

Research paper thumbnail of Optimal convergence rates for semidiscrete approximations of parabolic problems with nonsmooth boundary data

Http Dx Doi Org 10 1080 01630569108816443, May 15, 2007

ABSTRACT

Research paper thumbnail of Exponential decay for low and higher energies in the third order linear Moore-Gibson-Thompson equation with variable viscosity

ABSTRACT We consider the Moore-Gibson-Thompson equation which arises, e.g., as a linearization of... more ABSTRACT We consider the Moore-Gibson-Thompson equation which arises, e.g., as a linearization of a model for wave propagation in viscous thermally relaxing fluids. This third order in time equation displays, even in the linear version, a variety of dynamical behaviors for their solutions that depend on the physical parameters in the equation. These range from non-existence and instability to exponential stability (in time). By neglecting diffusivity of the sound coefficient there is a lack of generation of a semigroup associated with the linear dynamics. When diffusivity of the sound is positive, the linear dynamics is described by a strongly continuous evolution. We shall show that this evolution is exponentially stable provided sufficiently large viscous damping is accounted for in the model. The viscosity considered is time and space dependent which then leads to evolution rather then semigroup generators. Decay rates for both natural and higher level energies are derived.

Research paper thumbnail of Algebraic riccati equations with unbounded input → solution operator: applications to boundary control for wave and plate problems

Research paper thumbnail of Boundary control of parabolic systems: Regularity of optimal solutions

Appl Math Opt, 1977

... Irena Lasiecka Department of System Science, University of California at Los Angeles, Los Ang... more ... Irena Lasiecka Department of System Science, University of California at Los Angeles, Los Angeles, California ... coefficients in 9. Since T is assumed to be strongly elliptic, then there exists a constant a >0 such that the quadratic form N X aij~i~j > ot X ~i 2 for all ¢ E fL i=l i=l ...

Research paper thumbnail of Regularity and Strong Convergence of a Variational Approximation to a Nonhomogeneous Dirichlet Hyperbolic Boundary Value Problem

Siam Journal on Mathematical Analysis, Jul 17, 2006

Research paper thumbnail of Exponential local stability of first order strictly hyperbolic systems with nonlinear perturbations on the boundary

Lecture Notes in Control and Information Sciences, 1988

Research paper thumbnail of Exponential stabilization, via Riccati operator, of hyperbolic systems with uncontrolled, unbounded perturbations

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