Remarks on the Vol'pert Theory of Travelling-wave Solutions for Parabolic Systems

@inproceedings{CrooksRemarksOT,
  title={Remarks on the Vol'pert Theory of Travelling-wave Solutions for Parabolic Systems},
  author={Elaine Crooks}
}
Vol'pert and Vol'pert have shown that the parabolic system of n equations, @u @t = A @ 2 u @x 2 + f(u) has monotone travelling-wave solutions connecting two equilibria, S and T say, under `bistable' and`monostable' conditions on the function f : R n ! R n , when A is a positive-deenite diagonal matrix. We observe that this genre of hypotheses on f yields results on the existence and properties of intermediate zeros of f between S and T. These imply the existence of a `chain' of monotone… CONTINUE READING

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