Error Estimates for a Nonlinear Degenerate Parabolic Problem

Error estimates for a mixed finite element discretization of some degenerate parabolic equations

A priori estimates for quasilinear degenerate parabolic equations

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

L1–framework for Continuous Dependence and Error Estimates for Quasilinear Anisotropic Degenerate Parabolic Equations

We develop a general L–framework for deriving continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations with the aid of the Chen-Perthame kinetic approach [9]. We apply our L–framework to establish an explicit estimate for continuous dependence on the nonlinearities and an optimal error estimate for the vanishing anisotropic viscosity method, without t...

L–framework for Continuous Dependence and Error Estimates for Quasilinear Anisotropic Degenerate Parabolic Equations

We develop a general L1–framework for deriving continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations with the aid of the Chen-Perthame kinetic approach [9]. We apply our L1–framework to establish an explicit estimate for continuous dependence on the nonlinearities and an optimal error estimate for the vanishing anisotropic viscosity method, without...

A Blow-up Criterion for a Degenerate Parabolic Problem Due to a Concentrated Nonlinear Source

Let q, a, b, and T be real numbers with q ≥ 0, a > 0, 0 < b < 1, and T > 0. This article studies the following degenerate semilinear parabolic first initial-boundary value problem, xut(x, t)− uxx(x, t) = aδ(x− b)f (u(x, t)) for 0 < x < 1, 0 < t ≤ T, u(x, 0) = ψ(x) for 0 ≤ x ≤ 1, u(0, t) = u(1, t) = 0 for 0 < t ≤ T, where δ (x) is the Dirac delta function, and f and ψ are given functions. It is ...