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The energy method for elastic problems with non-homogeneous boundary conditions

100%

Quintanilla R.

International Journal of Applied Mathematics and Computer Science

2002

tom 12

nr 1

91-100

In this paper we propose the weighted energy method as a way to study estimates of solutions of boundary-value problems with non-homogeneous boundary conditions in elasticity. First, we use this method to study spatial decay estimates in two-dimensional elasticity when we consider non-homogeneous boundary conditions on the boundary. Some comments in the case of harmonic vibrations are considered as well. We also extend the arguments to a class of three-dimensional problems in a cylinder. A section is devoted to the study of an ill-posed problem. Some remarks are presented in the last section of the paper.

$L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

88%

Gawinecki J.

Annales Polonici Mathematici

1991

tom 54

nr 2

135-145

We prove the $L^p$-$L^q$-time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman's approach [12], [5] to the $L^p$-$L^q$-time decay estimates.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 International Journal of Applied Mathematics and Computer Science

1 Gawinecki J.

1 Quintanilla R.

1 2002

1 1991

Wyniki wyszukiwania

The energy method for elastic problems with non-homogeneous boundary conditions

$L^p$-$L^q$-Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity