Andreu, FuensantaCaselles, VicenteMazón, José2018-12-202018-12-202002Andreu 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/3140213-2230http://hdl.handle.net/10230/36166We 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.application/pdfeng© European Mathematical Society (EMS)info:eu-repo/semantics/articlehttp://dx.doi.org/10.4171/RMI/314Linear growth functionalsNonlinear parabolic equationsAccretive operatorsNonlinear semigroupsinfo:eu-repo/semantics/openAccess