Abstract
A reaction-diffusion equation with nonlinear boundary condition is considered in a two-dimensional infinite strip. Existence of waves in the bistable case is proved by the Leray-Schauder method.
Highlights
We will study the existence of travelling wave solutions of this problem, that is of solutions of the equation with the same boundary conditions
A reaction-diffusion system with nonlinear boundary conditions suggested as a model of atherosclerosis was studied in [3] in the monostable case
It is monotone and the L2 norm of the difference w2 − w1 is bounded since these functions approach exponentially their limits at infinity
Summary
The limiting functions are solutions of the following problem in the interval 0 ≤ y ≤ 1: u′′ + f (u) = 0,. V(x, y) ≡ 0, and we have proved that limiting problems do not have nonzero bounded solutions. This is true for the formally adjoint operator. It is proved that under condition (4) the operator P is proper in the weighted spaces and that the topological degree can be defined [7].
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