Complete quenching phenomenon for a parabolic p-Laplacian equation with a weighted absorption

Solutions with Dead Cores for a Parabolic P-Laplacian Equation

We study the solutions with dead cores and the decay estimates for a parabolic p-Laplacian equation with absorption by suband supersolution method. Special attention is given to the case where the solution of the steady-state problem vanishes in an interior region.

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

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...

SINGULAR SOLUTIONS OF PARABOLIC p-LAPLACIAN WITH ABSORPTION

We consider, for p ∈ (1, 2) and q > 1, the p-Laplacian evolution equation with absorption ut = div (|∇u|p−2∇u)− u in R × (0,∞). We are interested in those solutions, which we call singular solutions, that are non-negative, non-trivial, continuous in Rn × [0,∞) \ {(0, 0)}, and satisfy u(x, 0) = 0 for all x = 0. We prove the following: (i) When q ≥ p− 1 + p/n, there does not exist any such singul...

Existence of a positive solution for a p-Laplacian equation with‎ ‎singular nonlinearities

‎In this paper‎, ‎we study a class of boundary value problem‎ ‎involving the p-Laplacian oprator and singular nonlinearities‎. ‎We‎ ‎analyze the existence a critical parameter $lambda^{ast}$ such‎ ‎that the problem has least one solution for‎ ‎$lambdain(0,lambda^{ast})$ and no solution for‎ ‎$lambda>lambda^{ast}.$ We find lower bounds of critical‎ ‎parameter $lambda^{ast}$‎. ‎We use the method ...