Limiting behavior of strongly damped nonlinear wave equations
The author considers the equation: \(u_{tt}+\alpha Au_ t+Au=f(t,u,u_ t)\) where A is a sectorial operator on a Banach space, \(\alpha >0\) and f is a nonlinear operator periodic in t and satisfying some regularity and growth assumptions. He rewrites the equation as an abstract ordinary differential equation on a Banach space and he proves local existence, uniqueness and continuous dependence theorems. Some physical problems that are governed by an equation of this kind are also presented.
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