Existence of solutions for some 'noncoercive' parabolic equations

Maria Michaela Porzio

doi:10.3934/dcds.1999.5.553

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1999, Volume 5, Issue 3: 553-568. Doi: 10.3934/dcds.1999.5.553

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Existence of solutions for some "noncoercive" parabolic equations

Maria Michaela Porzio^1,

1.
Dipartimento di Matematica "G. Castelnuovo", Università degli Studi di Roma "La Sapienza", P.le A. Moro, 2 - 00185 Roma

Received: April 30, 1998

Revised: October 31, 1998

Published: June 1999

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Abstract

In this paper we prove the existence of a solution for a class of noncoercive Cauchy problems whose prototype is the boundary value problem

$\frac{\partialu}{\partial t}-$ div$(|Du|^{p-2}Du) + B(x, t)\cdot |Du|^{\gamma-1}Du = f$ in $\Omega_T$,

$u(x, t)=0$ on $\Omega\times (0, T),$

$u(x, 0) = u_0(x)$ in $\Omega,$

under suitable hypotheses on the data.

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Mathematics Subject Classification: 35B45, 35K55, 35K65.

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