Advances in Differential Equations and Control Processes
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Abstract: We use Nash’s inequality and a Moser-type iteration
to obtain a fundamental supnorm estimate 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. Initial states are assumed in for some
Keywords and phrases: a priori estimates, decay
rates, diffusion waves, heterogeneous media, anisotropic media, Moser iteration,
Nash’s inequality, behavior.
