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| EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELINGWAVE SOLUTIONS |
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Citation： |
ZHANG Linghai.EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELINGWAVE SOLUTIONS[J].Chinese Annals of Mathematics B,2001,22(3):343~360 |
| Page view： 1066
Net amount： 631 |
Authors： |
ZHANG Linghai; |
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| Abstract： |
This paper studies the asymptotic stability of traveling wave solutions of nonlinear systems
of integral-differential equations. It has been established that linear stability of traveling waves
is equivalent to nonlinear stability and some “nice structure” of the spectrum of an associated
operator implies the linear stability. By using the method of variation of parameter, the author
defines some complex analytic function, called the Evans function. The zeros of the Evans
function corresponds to the eigenvalues of the associated linear operator. By calculating the
zeros of the Evans function, the asymptotic stability of the traveling wave solutions is established. |
Keywords： |
Traveling wave solutions, Asymptotic stability, Eigenvalue problem, Normal
spectrum, Evans function |
Classification： |
35B25, 35K57, 35Q51 |
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