Global existence and blow-up for harmonic map heat flow

Blow-up and global existence for heat flows of harmonic maps

Infinite time blow - up for half - harmonic map flow from R into S 1 ∗

We study infinite time blow-up phenomenon for the half-harmonic map flow { ut = −(−∆) 1 2u+ ( 1 2π ∫ R |u(x)−u(s)| |x−s|2 ds ) u in R× (0,∞), u(·, 0) = u0 in R, (0.1) with a function u : R×[0,∞)→ S. Let q1, · · · , qk be distinct points in R, there exist an initial datum u0 and smooth functions ξj(t) → qj , 0 < μj(t) → 0, as t → +∞, j = 1, · · · , k, such that the solution uq of Problem (0.1) h...

Rigidity in the Harmonic Map Heat Flow

We establish various uniformity properties of the harmonic map heat ow, including uniform convergence in L 2 exponentially as t ! 1, and uniqueness of the positions of bubbles at innnite time. Our hypotheses are that the ow is between 2-spheres, and that the limit map and any bubbles share the same orientation.

Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with p-Laplacian with Nonlocal Sources

This paper deals with p-Laplacian systems ut − div(|∇u|p−2∇u) = ∫ Ωv α(x, t)dx, x ∈Ω, t > 0, vt − div(|∇v|q−2∇v) = ∫ Ωu β(x, t)dx, x ∈ Ω, t > 0, with null Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ RN , where p,q ≥ 2, α,β ≥ 1. We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow ...