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Well-posedness for a class of nonlinear degenerate parabolic equations. (English) Zbl 1381.35087
Summary: In this paper we obtain well-posedness for a class of semilinear weakly degenerate reaction-diffusion systems with Robin boundary conditions. This result is obtained through a Gagliardo-Nirenberg interpolation inequality and some embedding results for weighted Sobolev spaces.

MSC:
35K57 Reaction-diffusion equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35K58 Semilinear parabolic equations
35K65 Degenerate parabolic equations
35K90 Abstract parabolic equations
35K45 Initial value problems for second-order parabolic systems
35K55 Nonlinear parabolic equations
35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations
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References:
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