- Journal Home
- Volume 37 - 2024
- Volume 36 - 2023
- Volume 35 - 2022
- Volume 34 - 2021
- Volume 33 - 2020
- Volume 32 - 2019
- Volume 31 - 2018
- Volume 30 - 2017
- Volume 29 - 2016
- Volume 28 - 2015
- Volume 27 - 2014
- Volume 26 - 2013
- Volume 25 - 2012
- Volume 24 - 2011
- Volume 23 - 2010
- Volume 22 - 2009
- Volume 21 - 2008
- Volume 20 - 2007
- Volume 19 - 2006
- Volume 18 - 2005
- Volume 17 - 2004
- Volume 16 - 2003
- Volume 15 - 2002
- Volume 14 - 2001
- Volume 13 - 2000
- Volume 12 - 1999
- Volume 11 - 1998
- Volume 10 - 1997
- Volume 9 - 1996
- Volume 8 - 1995
- Volume 7 - 1994
- Volume 6 - 1993
- Volume 5 - 1992
- Volume 4 - 1991
- Volume 3 - 1990
- Volume 2 - 1989
- Volume 1 - 1988
Lp-Lq Estimates for a Linear Perturbed Klein-Gordon Equation
Cited by
Export citation
- BibTex
- RIS
- TXT
@Article{JPDE-8-341,
author = {Chunlai Mu },
title = {Lp-Lq Estimates for a Linear Perturbed Klein-Gordon Equation},
journal = {Journal of Partial Differential Equations},
year = {1995},
volume = {8},
number = {4},
pages = {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.},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5666.html}
}
TY - JOUR
T1 - Lp-Lq Estimates for a Linear Perturbed Klein-Gordon Equation
AU - Chunlai Mu
JO - Journal of Partial Differential Equations
VL - 4
SP - 341
EP - 350
PY - 1995
DA - 1995/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5666.html
KW - L^p-L^q estimates
KW - Klein-Gordon equation
KW - perturbed potential
AB - 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.
Chunlai Mu . (1995). Lp-Lq Estimates for a Linear Perturbed Klein-Gordon Equation.
Journal of Partial Differential Equations. 8 (4).
341-350.
doi:
Copy to clipboard