Blow up of Solutions with Positive Initial Energy for the Nonlocal Semilinear Heat Equation

Blow-up of a nonlocal semilinear parabolic equation with positive initial energy

Roles of Weight Functions to a Nonlocal Porous Medium Equation with Inner Absorption and Nonlocal Boundary Condition

and Applied Analysis 3 He studied the asymptotic behavior of solutions and found the influence of weight function on the existence of global and blow-up solutions. Wang et al. 10 studied porous medium equation with power form source term ut Δu u, x, t ∈ Ω × 0, ∞ , 1.8 subjected to nonlocal boundary condition 1.2 . By virtue of the method of upper-lower solutions, they obtained global existence,...

Blow-up of Solutions of a Semilinear Heat Equation with a Visco-elastic Term

In this work we consider an initial boundary value problem related to the equation ut −∆u+ ∫ t 0 g(t− s)∆u(x, s)ds = |u|p−2u and prove, under suitable conditions on g and p, a blow-up result for solutions with negative or vanishing initial energy. This result improves an earlier one by the author. Mathematics Subject Classification (2000). 35K05 35K65.

Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition

In this paper, we consider a semilinear parabolic equation ut = ∆u + u q ∫ t 0 u(x, s)ds, x ∈ Ω, t > 0 with nonlocal nonlinear boundary condition u|∂Ω×(0,+∞) = ∫ Ω φ(x, y)u (y, t)dy and nonnegative initial data, where p, q ≥ 0 and l > 0. The blow-up criteria and the blow-up rate are obtained.

A Class of Nonlocal Coupled Semilinear Parabolic System with Nonlocal Boundaries

We investigate the positive solutions of the semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal Dirichlet boundary conditions. The blow-up and global existence criteria are obtained.