Abstract

The mixed problem for nonlinear strongly dissipative wave equations with acoustic transmission conditions is considered. An existence and uniqueness theorem for local solutions is proved using the Faedo–Galerkin approximations, the compactness method, and the fixed point theorem. The existence of global solutions of this problem is also proved.

中文翻译：

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非线性传播条件下强耗散波方程解的存在性

摘要

考虑具有声传输条件的非线性强耗散波动方程的混合问题。使用Faedo-Galerkin逼近，紧致法和不动点定理证明了局部解的存在性和唯一性定理。还证明了该问题的整体解决方案的存在。