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Remarks on Fourier multipliers and applications to the wave equation. (English) Zbl 1164.35052

Actually one considers the Cauchy Problem for the wave equation with a nonlinear forcing term \(F(u)\) which is an entire analytic function. The well-posedness of the Cauchy problem in some modulation spaces is proved. A special discussion is done for the case \(F(u)\) is of a power nonlinearity, where the well-posedness could be proved in Wiener amalgam spaces. The proof of results uses Fourier multiplier estimates in modulation spaces.

MSC:

35L05 Wave equation
35L15 Initial value problems for second-order hyperbolic equations
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References:

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