<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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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