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Interfacial phenomena of the forward backward convection-diffusion equations. (English) Zbl 1381.35093

Summary: This paper is devoted to the interfacial phenomena of a class of forward backward convection-diffusion equations. Under the assumption that the equations have classical solutions, we prove that the forward region expands with a positive rate in one dimension.

MSC:

35K59 Quasilinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
35R35 Free boundary problems for PDEs
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