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Zbl 1212.35268
Agre, Keith; Rammaha, M.A.
Systems of nonlinear wave equations with damping and source terms. (English)
[J] Differ. Integral Equ. 19, No. 11, 1235-1270 (2006). ISSN 0893-4983

Summary: In this article we focus on the global well posedness of the system of nonlinear wave equations $u_{tt}-\Delta u+\vert u_t\vert ^{m-1}u_t=f_1(u,v)$, $v_{tt}-\Delta v+\vert v_t\vert ^{r-1}v_t=f_2(u,v)$ in a bounded domain $\Omega \subset \Bbb R^n$, $n=1,2,3$, with Dirichlet boundary conditions. Under some restriction on the parameters in the system we obtain several results on the existence of local and global solutions, uniqueness and the blow up of solutions in finite time.

MSC 2000:: *35L05 Wave equation
35L20 Second order hyperbolic equations, boundary value problems

Keywords: global well posedness; system of nonlinear wave equations; blow up in finite time

Cited in: Zbl 1246.35039 Zbl 1230.35062 Zbl 1240.35342

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