L\({}^ p-L^ q\)-time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity. (English) Zbl 0732.73001
For the Cauchy problem to the system of equations
\[
\rho \partial^ 2_ tu-\mu \Delta u-(\lambda +\mu)\text{grad} div u+\beta \text{grad} \partial_ tT=0,\quad \beta div \partial_ tu+\rho \tau \partial^ 2_ tT-k\Delta T=0
\]
of linear thermoelasticity \(L^ p-L^ q\) time- decay estimates are proved. Such estimates are needed to prove global existence in time to the Cauchy problem for the equations of nonlinear thermoelasticity.
Reviewer: H.-D.Alber (Darmstadt)
MSC:
| 74A15 | Thermodynamics in solid mechanics |
| 35A07 | Local existence and uniqueness theorems (PDE) (MSC2000) |
| 35G15 | Boundary value problems for linear higher-order PDEs |
| 35L40 | First-order hyperbolic systems |
| 35L45 | Initial value problems for first-order hyperbolic systems |
| 35E05 | Fundamental solutions to PDEs and systems of PDEs with constant coefficients |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 74B05 | Classical linear elasticity |
