Saddle solutions of the bistable diffusion equation. (English) Zbl 0764.35048

Summary: Stationary solutions of the bistable Cahn-Allen diffusion equation in the plane are constructed, which are positive in quadrants 1 and 3 and negative in the other two quadrants. They are unique and obey certain monotonicity and limiting properties. Solutions of the dynamic problem near this stationary solution generally split the cross-shaped nullset into two disconnected parts which remain bounded away from each other.


35K55 Nonlinear parabolic equations
35B20 Perturbations in context of PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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