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 \(L^1\) for these solutions. To prove the existence we use the nonlinear semigroup theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 26 October 2000 / Revised version: 1 May 2001 / Published online: 24 September 2001
Rights and permissions
About this article
Cite this article
Andreu-Vaillo, F., Caselles, V. & Mazón, J. Existence and uniqueness of a solution for a parabolic quasilinear problem for linear growth functionals with $L^1$ data. Math Ann 322, 139–206 (2002). https://doi.org/10.1007/s002080100270
Issue Date:
DOI: https://doi.org/10.1007/s002080100270