Blow-up of generalized solutions to wave equations with nonlinear degenerate damping and source terms
Viorel BarbuIrena LasieckaMohammad Rammaha
35L0535L2058G16wave equationsdamping and source termsweak solutionssubdifferentialblow-up of solutionsenergy estimates
This article is concerned with the blow-up of \textit{generalized} solutions to the wave equation $u_{tt} - \Delta u + |u|^k j'(u_t) = |u|^{p-1} u$ in $\Omega \times (0,T)$, where $p > 1$ and $ j'$ denotes the derivative of a $C^1$ convex and real valued function $j$. We prove that every generalized solution to the equation that enjoys an additional regularity blows-up in finite time; whenever the exponent $p$ is greater than the critical value $k + m$, and the initial energy is negative.
Indiana University Mathematics Journal
2007
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10.1512/iumj.2007.56.2990
10.1512/iumj.2007.56.2990
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Indiana Univ. Math. J. 56 (2007) 995 - 1022
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