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Periodic travelling wave solutions of a parabolic equation: a monotonicity result. (English) Zbl 1072.35539
Summary: This paper considers travelling wave solutions of a quasilinear parabolic equation corresponding to the propagation of a front in some striated medium: \[ \xi_t+R(y\sin\alpha-\xi\cos\alpha)\sqrt{1+\xi_y^2}=\nu\xi_{yy},\quad y\in\mathbb R, t\in\mathbb R.\tag{1} \] The striations, whose geometry play a crucial role on the type of solutions obtained, are supposed to be oblique and disposed in a periodic fashion. We show that the speed of such travelling waves depends in a monotonous way on the angle of inclination of the striations.

35K55 Nonlinear parabolic equations
34B15 Nonlinear boundary value problems for ordinary differential equations
35B10 Periodic solutions to PDEs
Full Text: DOI
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