Small data global existence for the semilinear wave equation with space-time dependent damping

Details Small data global existence for the semilinear wave equation with space-time dependent damping Small data global existence for the semilinear wave equation with space-time dependent damping

2012-02-24

arxiv.org/abs/1202.5379v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we consider the critical exponent problem for the semilinear wave equation with space-time dependent damping. When the damping is effective, it is expected that the critical exponent agrees with that of only space dependent coefficient case. We shall prove that there exists a unique global solution for small data if the power of nonlinearity is larger than the expected exponent. Moreover, we do not assume that the data are compactly supported. However, it is still open whether there exists a blow-up solution if the power of nonlinearity is smaller than the expected exponent.

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