A Parabolic quasilinear problem for linear growth functionals

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, wh...

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Detalles Bibliográficos
Autores: Andreu, Fuensanta, Caselles, Vicente, Mazón, José
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2002
País:España
Institución:Universitat Pompeu Fabra
Repositorio:Repositorio Digital de la UPF
OAI Identifier:oai:repositori.upf.edu:10230/36166
Acceso en línea:http://hdl.handle.net/10230/36166
http://dx.doi.org/10.4171/RMI/314
Access Level:acceso abierto
Palabra clave:Linear growth functionals
Nonlinear parabolic equations
Accretive operators
Nonlinear semigroups
Descripción
Sumario: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.