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Decay estimates for solutions of quasilinear parabolic equations in heterogeneous media. (English) Zbl 1219.35025
The authors are interested to prove some $$L^\infty$$ estimates for solutions of the Cauchy problem for second-order quasilinear parabolic equations in general heterogeneous media, under some requirements on the viscosity tensor and the advection velocity field. They prove this result by using Nash’s inequality and a Moser-type iteration. Initial data are assumed in $$L^{p}(\mathbb R)^n$$ for some $$1\leq p < \infty$$.

MSC:
 35B40 Asymptotic behavior of solutions to PDEs 35B45 A priori estimates in context of PDEs 35K15 Initial value problems for second-order parabolic equations 35K59 Quasilinear parabolic equations
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