Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations
نویسندگان
چکیده
We consider the semilinear parabolic equation ut = uxx + f(u), x ∈ R, t > 0, (A) where f is a bistable nonlinearity. It is well-known that for a large class of initial data, the corresponding solutions converge to traveling fronts. We give a new proof of this classical result as well as some generalizations. Our proof uses a geometric method, which makes use of spatial trajectories {(u(x, t), ux(x, t)) : x ∈ R} of solutions of (A).
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