6533b853fe1ef96bd12ad33e

RESEARCH PRODUCT

Existence and uniqueness of a solution for a parabolic quasilinear problem for linear growth functionals with $L^1$ data

Vicent Caselles CostaFuensanta Andreu VaílloJosé Manuel Mazón Ruiz

subject

Dirichlet problemNonlinear systemSpacetimeSemigroupGeneral MathematicsMathematical analysisMathematics::Analysis of PDEsUniquenessLinear growthParabolic partial differential equationMathematicsEnergy functional

description

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.

yearjournalcountryeditionlanguage
2002-01-01Mathematische Annalen
https://doi.org/10.1007/s002080100270