BLOW-UP RESULTS FOR A VISCOELASTIC PLATE EQUATION WITH DISTRIBUTED DELAY

A Blow-up Result for a Viscoelastic System in R

In this paper we consider a coupled system of nonlinear viscoelastic equations. Under suitable conditions on the initial data and the relaxation functions, we prove a finite-time blow-up result.

Multiple blow-up for a porous medium equation with reaction

The present paper is concerned with the Cauchy problem { ∂tu = ∆u + u in R × (0,∞), u(x, 0) = u0(x) ≥ 0 in R , with p,m > 1. A solution u with bounded initial data is said to blow up at a finite time T if lim supt↗T ‖u(t)‖L∞(RN ) = ∞. For N ≥ 3 we obtain, in a certain range of values of p, weak solutions which blow up at several times and become bounded in intervals between these blow-up times....

Blow-up for a reaction-diffusion equation with variable coefficient

We study the blow-up behavior for positive solutions of a reaction–diffusion equationwith nonnegative variable coefficient. When there is no stationary solution, we show that the solution blows up in finite time. Under certain conditions, we then show that any point with zero source cannot be a blow-up point. © 2012 Elsevier Ltd. All rights reserved.

Blow-Up Results for a Nonlinear Hyperbolic Equation with Lewis Function

Blow-up for the 1d Nonlinear Schrödinger Equation with Point Nonlinearity Ii: Supercritical Blow-up Profiles

We consider the 1D nonlinear Schrödinger equation (NLS) with focusing point nonlinearity, (0.1) i∂tψ + ∂ 2 xψ + δ|ψ|p−1ψ = 0, where δ = δ(x) is the delta function supported at the origin. In the L supercritical setting p > 3, we construct self-similar blow-up solutions belonging to the energy space Lx ∩Ḣ x. This is reduced to finding outgoing solutions of a certain stationary profile equation. ...