A quasilinear parabolic perturbation of the linear heat equation

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

A quasilinear parabolic singular perturbation problem

in a pointwise sense and in a viscosity sense. Here uν denotes the derivative of u with respect to the inward unit spatial normal ν to the free boundary ∂{u > 0}, M = ∫ β(s) ds, α(ν,M) := Φ−1 ν (M) andΦν(α) := −A(αν)+αν ·F(αν), where A(p) is such that F(p) = ∇A(p) with A(0) = 0. Some of the results obtained are new even when the operator under consideration is linear. 2000 Mathematics Subject C...

Quenching Profile for a Quasilinear Parabolic Equation

where 00, Z>0, and uq(x) >0, Vx G [—1, Z]. Without loss of generality, we may assume that uq(x) is smooth and bounded above by 1 such that uo(±Z) = 1. Since uo(x) is positive, the local (in time) existence and uniqueness of a classical solution of the problem (1.1)—(1.3) are trivial (see [8]). Many results in quenching, such as single point quenching and profiles, are similar to those b...

Rational Approximation for a Quasilinear Parabolic Equation

Approximation theorems, analogous to known results for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for a nonlinear parabolic equation, Burgers’ equation.

a quasilinear parabolic equation with inhomogeneous density and absorption