JournalsrmiVol. 18, No. 1pp. 135–185

A Parabolic Quasilinear Problem for Linear Growth Functionals

  • Fuensanta Andreu

    Universitat de Valencia, Burjassot (Valencia), Spain
  • Vicent Caselles

    Universitat Pompeu-Fabra, Barcelona, Spain
  • José M. Mazón

    Universitat de Valencia, Burjassot (Valencia), Spain
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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+ξ2f(x, \xi) = \sqrt{1 + \Vert \xi \Vert^2}, which corresponds with the time-dependent minimal surface equation. We also study the asymptotic behaviour of the solutions.

Cite this article

Fuensanta Andreu, Vicent Caselles, José M. Mazón, A Parabolic Quasilinear Problem for Linear Growth Functionals. Rev. Mat. Iberoam. 18 (2002), no. 1, pp. 135–185

DOI 10.4171/RMI/314