REGULARITY AND BLOW-UP CONSTANTS OF SOLUTIONS FOR NONLINEAR DIFFERENTIAL EQUATION

Blow-up of Solutions for an Integro-differential Equation with a Nonlinear Source

We study the nonlinear viscoelastic wave equation

Blow-up of solutions to a nonlinear dispersive rod equation

In this paper, firstly we find the best constant for a convolution problem on the unit circle via a variational method. Then we apply the best constant on a nonlinear rod equation to give sufficient conditions on the initial data, which guarantee finite time singularity formation for the corresponding solutions. Mathematics Subject Classification(2000): 30C70, 37L05, 35Q58, 58E35

Blow-up solutions of nonlinear Volterra integro-differential equations

The paper studies the finite-time blow-up theory for a class of nonlinear Volterra integro-differential equations. The conditions for the occurrence of finite-time blow-up for nonlinear Volterra integro-differential equations are provided. Moreover, the finite-time blow-up theory for nonlinear partial Volterra integro-differential equations with general kernels is also established using the blo...

Blow up and regularity for fractal Burgers equation

The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existence of the finite time blow up for the power of Laplacian α < 1/2, and global existence as well as analyticity of solution for α ≥ 1/2. We also prove the existence of solutions with very rough initial data u0 ∈ Lp, 1 ...

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow