L 1 -Contraction and Uniqueness for Quasilinear Elliptic-Parabolic Equations

Author: Otto F.  

Publisher: Academic Press

ISSN: 0022-0396

Source: Journal of Differential Equations, Vol.131, Iss.1, 1996-10, pp. : 20-38

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Abstract

We prove the L 1 -contraction principle and uniqueness of solutions for quasilinear elliptic-parabolic equations of the form partial_t[b(u)]-{rom div}[a( abla u, b(u))]+f(b(u))=0qquad mbox{in}quad (0, T)timesOmega, where b is monotone nondecreasing and continuous. We assume only that u is a weak solution of finite energy. In particular, we do not suppose that the distributional derivative ∂ t [ b ( u )] is a bounded Borel measure or a locally integrable function.