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Well-posedness for the 2-D damped wave equations with exponential source terms

✍ Scribed by Xiaosen Han; Mingxin Wang

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 213 KB
Volume: 33
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1320

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✦ Synopsis

Communicated by P. Sacks

In this paper we study well-posedness of the damped nonlinear wave equation

in X×(0, ∞) with initial and Dirichlet boundary condition, where X is a bounded domain in R 2 ; x ≥ 0, xk 1 +l>0 with k 1 being the first eigenvalue of -D under zero boundary condition. Under the assumptions that g(•) is a function with exponential growth at the infinity and the initial data lie in some suitable sets we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property and uniform decay estimates of the energy.

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