127 research outputs found
Semi-linear wave equations with effective damping
We study the Cauchy problem for the semi-linear damped wave equation in any
space dimension. We assume that the time-dependent damping term is effective.
We prove the global existence of small energy data solutions in the
supercritical case.Comment: 28 page
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In this note we study the global existence of small data solutions to the
Cauchy problem for the semi-linear wave equation with a not effective
scale-invariant damping term, namely where , . We
prove blow-up in finite time in the subcritical range and an
existence result for , . In this way we find the critical
exponent for small data solutions to this problem. All these considerations
lead to the conjecture for , where is the
Strauss exponent for the classical wave equation
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