Nonlinear wave equation



Nonlinear wave equation

A general nonlinear wave equation can be expressed as

(NWE){utt-uxx=f(x,t,u) in (0,π)×u(0,t)=u(π,t)=0t

where f(x,t,s) is a continuousMathworldPlanetmath, monotonic increasing or decreasing (in s) real function on [0,π]×2 and 2π-periodic in t. Nontrivial periodic solutions are of interest in many applications. Existence of multiple or even infinitely many periodic solutions to some special cases of (NWE), e.g., f(x,t,s) is superlinear in s and/or independent of the time t, have been proved by many authors such as P. Rabinowitz, V. Benci, M. Berti, etc.

Title Nonlinear wave equation
Canonical name NonlinearWaveEquation1
Date of creation 2013-03-11 19:28:45
Last modified on 2013-03-11 19:28:45
Owner linor (11198)
Last modified by (0)
Numerical id 1
Author linor (0)
Entry type Definition