Revista Matemática Iberoamericana


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Volume 18, Issue 1, 2002, pp. 135–185
DOI: 10.4171/RMI/314

Published online: 2002-04-30

A Parabolic Quasilinear Problem for Linear Growth Functionals

Fuensanta Andreu[1], Vicent Caselles and José M. Mazón[2]

(1) Universitat de Valencia, Burjassot (Valencia), Spain
(2) Universitat de Valencia, Burjassot (Valencia), Spain

We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. A typical example of energy functional we consider is the one given by the nonparametric area integrand $f(x, \xi) = \sqrt{1 + \Vert \xi \Vert^2}$, which corresponds with the time-dependent minimal surface equation. We also study the asymptotic behaviour of the solutions.

Keywords: Linear growth functionals, nonlinear parabolic equations, accretive operators, nonlinear semigroups

Andreu Fuensanta, Caselles Vicent, Mazón José: A Parabolic Quasilinear Problem for Linear Growth Functionals. Rev. Mat. Iberoamericana 18 (2002), 135-185. doi: 10.4171/RMI/314