Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping

By Lorena Bociu, Irena Lasiecka. 2008

53 citations recorded by the source corpus.

We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely p > m and k > m), weak solutions blow up in finite time.

Subfields: Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2521e3f0f860a7bb58ba18d7055dd7a0758f473e

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In Control and Systems Engineering

1. Lorena Bociu
2. Mohammad Rammaha
3. Daniel Toundykov
4. Irena Lasiecka

In Mathematical Physics

1. Lorena Bociu
2. Daniel Toundykov
3. Mohammad Rammaha
4. Irena Lasiecka

Citations in the corpus

• On a wave equation with supercritical interior and boundary sources and damping terms (2011, background): “Moreover, we establish a new blow up result for initial data of non-negative energy, thus complementing the theorem in [8] which is valid only for initial data of negative energy.”