A Parabolic quasilinear problem for linear growth functionals

Andreu, Fuensanta; Caselles, Vicente; Mazón, José

doi:http://dx.doi.org/10.4171/RMI/314

A Parabolic quasilinear problem for linear growth functionals

Citation

Andreu F, Caselles V, Mazón JM. A Parabolic quasilinear problem for linear growth functionals. Revista Matemática Iberoamericana. 2002 Abr 30;18(1):135-58. DOI: 10.4171/RMI/314

Abstract

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,ξ)=√1+∥ξ∥2, which corresponds with the time-dependent minimal surface equation. We also study the asymptotic behaviour of the solutions.