2026-04-17T02:37:05Zhttps://recercat.cat/oai/request

oai:recercat.cat:10230/361662025-12-20T16:48:24Zcom_2072_6col_2072_452952

00925njm 22002777a 4500 dc Andreu, Fuensanta author Caselles, Vicente author Mazón, José author 2018-12-20T15:43:25Z 2018-12-20T15:43:25Z 2002 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. Linear growth functionals Nonlinear parabolic equations Accretive operators Nonlinear semigroups A Parabolic quasilinear problem for linear growth functionals