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Existence and stability of travelling wave solutions of competition models with migration effects. (English) Zbl 0751.92015
A two-species competition model with migration effects is considered, based on a semilinear hyperbolic system of partial differential equations. Travelling wave solutions are shown to exist, and the \(C^ 0\)-stability of these solutions is demonstrated. The asymptotic behaviour of some of these solutions is investigated.
A useful comparison theorem is established for a class of semilinear hyperbolic systems. Under certain conditions a solution which is initially “less” than another will remain so for all time.
Reviewer: J.H.Swart (Durban)
MSC:
92D40 Ecology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35L45 Initial value problems for first-order hyperbolic systems
92D25 Population dynamics (general)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B35 Stability in context of PDEs
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