Self-similar singular solutions of a p-Laplacian evolution equation with absorption

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...

Solutions for singular p-Laplacian equation in Rn

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 ...

Vast Multiplicity of Very Singular Self-similar Solutions of a Semilinear Higher-order Diffusion Equation with Time-dependent Absorption

As a basic model, the Cauchy problem in R × R+ for the 2mth-order semilinear parabolic equation of the diffusion-absorption type ut = −(−∆) u− t|u|u, with p > 1, α > 0, m ≥ 2, with singular initial data u0 6= 0 such that u0(x) = 0 for any x 6= 0 is studied. The additional multiplier h(t) = t → 0 as t → 0 in the absorption term plays a role of timedependent non-homogeneous potential that affects...

Extinction and decay estimates of solutions for a p-Laplacian evolution equation with nonlinear gradient source and absorption

*Correspondence: [email protected] 2School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, P.R. China Full list of author information is available at the end of the article Abstract We investigate the extinction properties of non-negative nontrivial weak solutions of the initial-boundary value problem for a p-Laplacian evolution equation with nonlinear gradient source...