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)×ℝu(0,t)=u(π,t)=0∀t∈ℝ |
where f(x,t,s) is a continuous, monotonic increasing or decreasing (in s)
real function on [0,π]×ℝ2 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 |