In this work, the nonexistence of the global solutions to initial boundary value problems with dissipative terms in the boundary conditions is considered for a class of quasilinear hyperbolic equations. The nonexistence proof is achieved by the usage of the so-called concavity method. In this method
Nonexistence of global solutions of a hyperbolic problem
โ Scribed by M. Aassila
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 461 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0895-7177
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โฆ Synopsis
In this paper, we prove some blow-up results for the solutions of a semilinear hyperbolic problem with boundary conditions of memory type.
๐ SIMILAR VOLUMES
where t, ls a homogeneous linear partial differential operator of order m and p > 1. For example, we prove that for any T > 0 the problem, with ut(x,O) = ~1, cp(r) = lrlQ-%, 0 < q 5 1 and h(x) = 1x17, 7 > 0, has no solution if liml,+m ,,(x)lxl7q/(p-q) = 00.
In this paper the non-existence of global solutions of two fourth-order hyperbolic equations with dynamic boundary conditions is considered. The method of proof makes use of the generalized convexity method due to LADYZHENSKAYA and KALANTAROV [4].