TY - JOUR

T1 - Spatial trajectories and convergence to traveling fronts for bistable reaction-diffusion equations

AU - Poláčik, Peter

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We consider the semilinear parabolic equation ut = uxx + f(u), x∈ ℝ, t > 0, 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 (1).

AB - We consider the semilinear parabolic equation ut = uxx + f(u), x∈ ℝ, t > 0, 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 (1).

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U2 - 10.1007/978-3-319-19902-3_24

DO - 10.1007/978-3-319-19902-3_24

M3 - Article

AN - SCOPUS:85035078427

VL - 86

SP - 405

EP - 423

JO - Progress in Nonlinear Differential Equations and Their Application

JF - Progress in Nonlinear Differential Equations and Their Application

SN - 1421-1750

ER -