×

Correctors for the homogenization of some semilinear wave equations. (English) Zbl 0948.35014

Summary: We deal with the corrector’s problem for the homogenization of initial boundary value problems of the type \[ \begin{aligned} \rho^\varepsilon (x){\partial^2 u^\varepsilon \over\partial t^2}-\text{div} \bigl(A^\varepsilon (x)\nabla u^\varepsilon \bigr)+f(x,u^\varepsilon)= g(x,t) \quad & \text{in }\Omega \times(0,T),\\ u^\varepsilon(x,t) =0\quad & \text{on }\partial\Omega \times(0,T),\\ u^\varepsilon(x,0)= a^\varepsilon(x)\quad & \text{in }\Omega.\\ {\partial u^\varepsilon\over \partial t}(x,0)= b^\varepsilon(x) \quad &\text{in }\Omega.\end{aligned} \] in which the initial value is \(H^1_0\).

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L70 Second-order nonlinear hyperbolic equations
PDFBibTeX XMLCite