$L^{\infty }$ decay estimates of solutions of nonlinear parabolic equation release_sjq2cb5rfvdwxa3tpv54epyt3i

Abstract

<jats:title>Abstract</jats:title>In this paper, we are interested in <jats:inline-formula><jats:alternatives><jats:tex-math>$L^{\infty }$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>∞</mml:mi> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution <jats:italic>m</jats:italic>-Laplacian equation not in the divergence form. By a modified Moser's technique we obtain <jats:inline-formula><jats:alternatives><jats:tex-math>$L^{\infty }$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>∞</mml:mi> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> decay estimates of weak solutiona.
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