<em>L<sup>p</sup></em>-<em>L<sup>q</sup></em> Estimates for a Linear Perturbed Klein-Gordon Equation

<em>L<sup>p</sup></em>-<em>L<sup>q</sup></em> Estimates for a Linear Perturbed Klein-Gordon Equation

Year:    1995

Journal of Partial Differential Equations, Vol. 8 (1995), Iss. 4 : pp. 341–350

Abstract

We consider L^p-L^q estimates for the solution u(t,x) to tbe following perturbed Klein-Gordon equation ∂_{tt}u - Δu + u + V(x)u = 0 \qquad x∈ R^n, n ≥ 3 u(x,0) = 0, ∂_tu(x,0) = f(x) We assume that the potential V(x) and the initial data f(x) are compact, and V(x) is sufficiently small, then the solution u(t,x) of the above problem satisfies ||u(t)||_q ≤ Ct^{-a}||f||_p for t > 1 where a is the piecewise-linear function of 1/p and 1/q.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1995-JPDE-5666

Journal of Partial Differential Equations, Vol. 8 (1995), Iss. 4 : pp. 341–350

Published online:    1995-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    L^p-L^q estimates