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Control of blow-up singularities for nonlinear wave equations

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  • While the global boundary control of nonlinear wave equations that exhibit blow-up is generally impossible, we show on a typical example, motivated by laser breakdown, that it is possible to control solutions with small data so that they blow up on a prescribed compact set bounded away from the boundary of the domain. This is achieved using the representation of singular solutions with prescribed blow-up surface given by Fuchsian reduction. We outline on this example simple methods that may be of wider applicability.
    Mathematics Subject Classification: Primary: 93B05, 93C20; Secondary: 35L71.

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