Existence and uniqueness of a solution for a parabolic quasilinear problem for linear growth functionals with
$L^1$ data |
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| Authors: | F Andreu-Vaillo V Caselles JM Mazón |
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| Institution: | (1) Universitat de Valencia, 46100 Burjassot (Valencia), Spain (e-mail: Fuensanta.Andreu@uv.es, mazon@uv.es), ES;(2) Universitat Pompeu-Fabra, Passeig de Circumvalacio 8, 08003 Barcelona, Spain (e-mail: vicent.caselles@tecn.upf.es), ES |
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| Abstract: | We introduce a new concept of solution for the Dirichlet problem for quasilinear parabolic equations in divergent form for
which the energy functional has linear growth. Using Kruzhkov's method of doubling variables both in space and time we prove
uniqueness and a comparison principle in for these solutions. To prove the existence we use the nonlinear semigroup theory.
Received: 26 October 2000 / Revised version: 1 May 2001 / Published online: 24 September 2001 |
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| Keywords: | Mathematics Subject Classification (2000): 35K55 35K65 47H06 47H20 |
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