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Zbl 1190.35145
Wu, Jieqiong; Li, Shengjia; Chai, Shugen
Existence and nonexistence of a global solution for coupled nonlinear wave equations with damping and source. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 11, 3969-3975 (2010). ISSN 0362-546X

Summary: We consider the system of nonlinear wave equations $$\left.\aligned u_{tt}+|u_t|^{m-1}u_t&= \text{div}(\rho(|\nabla u|^2)\nabla u)+ f_1(u,v)\\ v_{tt}+|v_t|^{r-1}v_t&= \text{div}(\rho(|\nabla v|^2)\nabla v)+ f_1(u,v) \endaligned\right\} (x,t)\in\Omega\times(0,T),$$ with initial and Dirichlet boundary conditions. Under some suitable assumptions on the functions $f_1$ and $f_2$, the initial data and the parameters in the equations, the theorems of global existence and nonexistence are proved.

MSC 2000:: *35L53
35L72
35B44

Keywords: nonlinear wave equations; global existence; nonexistence

Cited in: Zbl 1232.35008

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