Spatial critical points of solutions of a one-dimensional nonlinear parabolic problem

Turyn, Lawrence

doi:10.1090/S0002-9939-1989-0961417-5

Spatial critical points of solutions of a one-dimensional nonlinear parabolic problem
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by Lawrence Turyn PDF

Proc. Amer. Math. Soc. 106 (1989), 1003-1009 Request permission

Abstract:

The number of spatial critical points is nonincreasing in time, for positive, analytic solutions of a scalar, nonlinear, parabolic partial differential equation in one space dimension. While proving this, we answer the question: What happens to a critical point which loses simplicity?

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