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Global smooth solutions to a class of semilinear wave equaiions with strong nonlinearities

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Abstract

We consider the Cauchy problem for semilinear wave equationsu tt−Δu=g(u) in 3+1 dimensions with smooth but possibly large data. Ifg isC 2,α and bounded from above everywhere and from below for negative arguments the existence of a global classical solution is shown. If moreoverg is nonpositive and vanishes at least of order 2+∈ at the origin and if the data decay sufficiently rapidly at infinity the scattering operator exists.

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Pecher, H. Global smooth solutions to a class of semilinear wave equaiions with strong nonlinearities. Manuscripta Math 69, 71–92 (1990). https://doi.org/10.1007/BF02567913

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  • DOI: https://doi.org/10.1007/BF02567913

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