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 , which corresponds with the time-dependent minimal surface equation. We also study the asymptotic behaviour of the solutions.
Cite this article
Fuensanta Andreu, Vicent Caselles, José M. Mazón, A Parabolic Quasilinear Problem for Linear Growth Functionals. Rev. Mat. Iberoam. 18 (2002), no. 1, pp. 135–185DOI 10.4171/RMI/314