July  1999, 5(3): 553-568. doi: 10.3934/dcds.1999.5.553

Existence of solutions for some "noncoercive" parabolic equations

1. 

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

Received  May 1998 Revised  November 1998 Published  May 1999

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.

Citation: Maria Michaela Porzio. Existence of solutions for some "noncoercive" parabolic equations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 553-568. doi: 10.3934/dcds.1999.5.553
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