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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 \(1\leq p < \infty\).

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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