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Nonlinear hyperbolic smoothing at a focal point
Applied Math| Speaker: | Jianfeng Liang, UC Davis |
| Location: | 693 Kerr |
| Start time: | Fri, Oct 31 2003, 4:10PM |
We study an interesting smoothing effect for solutions to a semilinear dissipative wave equation. We constrcut solutions with a focusing wave of singularity along an incoming light cone. The singularities are focused and partially smoothed out at the tip of the cone under strong dissipation. The result provides a good example of what can arise in wave propagation under the simultaneous action of focusing and dissipation. The smoothing results are also sharp for self-similar solutions.