0000000000217034
AUTHOR
Fuensanta Andreu Vaíllo
showing 2 related works from this author
Local and nonlocal weighted pLaplacian evolution equations with Neumann boundary conditions
2011
In this paper we study existence and uniqueness of solutions to the local diffusion equation with Neumann boundary conditions and a bounded nonhomogeneous diffusion coefficient g ≥ 0, {ut = div (g|∇u|p-2∇u) in ]0; T[×Ωg|∇u|p-2u·n = 0 on ]0; T[×∂Ω; for 1 ≤ p < ∞. We show that a nonlocal counterpart of this diffusion problem is ut(t; x)= ∫ω J(x-y)g(x+y/2)|u(t; y)-u(t; x)| p-2 (u(t; y)-u(t; x)) dy in ]0; T[× Ω,where the diffusion coefficient has been reinterpreted by means of the values of g at the point x+y/2 in the integral operator. The fact that g ≥ 0 is allowed to vanish in a set of positive measure involves subtle difficulties, specially in the case p = 1.
Existence and uniqueness of a solution for a parabolic quasilinear problem for linear growth functionals with $L^1$ data
2002
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.