Displaying similar documents to “The Cauchy problem for the damped wave equation with polyharmonic initial conditions”

A parametrix construction for wave equations with C 1 , 1 coefficients

Hart F. Smith (1998)

Annales de l'institut Fourier

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In this article we give a construction of the wave group for variable coefficient, time dependent wave equations, under the hypothesis that the coefficients of the principal term possess two bounded derivatives in the spatial variables, and one bounded derivative in the time variable. We use this construction to establish the Strichartz and Pecher estimates for solutions to the Cauchy problem for such equations, in space dimensions n = 2 and n = 3 .

Strichartz Type Estimates for Oscillatory Problems for Semilinear Wave Equation

Di Pomponio, Stefania (2000)

Serdica Mathematical Journal

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The author is partially supported by: M. U. R. S. T. Prog. Nazionale “Problemi e Metodi nella Teoria delle Equazioni Iperboliche”. We treat the oscillatory problem for semilinear wave equation. The oscillatory initial data are of the type u(0, x) = h(x) + ε^(σ+1) * e^(il(x)/ε) * b0 (ε, x) ∂t u(0, x) = ε^σ * e^(il(x)/ε) * b1(ε, x). By using suitable variants of Strichartz estimate we extend the results from [6] on a priori estimates of the approximations of...