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A Parabolic quasilinear problem for linear growth functionals Andreu, Fuensanta Caselles, Vicente Mazón, José Linear growth functionals Nonlinear parabolic equations Accretive operators Nonlinear semigroups 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. The first and third authors have been partially supported by the Spanish DGICYT, Project PB98-1442. The second author acknowledges partial support by the TMR European Project “Viscosity Solutions and their Applications”, reference FMRX-CT98-0234 and the PNPGC, Project BFM 2000-0962-C02-01. 2018-12-20T15:43:25Z 2018-12-20T15:43:25Z 2002 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion 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 0213-2230 http://hdl.handle.net/10230/36166 http://dx.doi.org/10.4171/RMI/314 eng Revista Matemática Iberoamericana. 2002 Abr 30;18(1):135-58. © European Mathematical Society (EMS) info:eu-repo/semantics/openAccess application/pdf application/pdf European Mathematical Society (EMS)