Blow-up for a degenerate parabolic equation with a nonlocal source

In this paper, we investigate the blowup properties of the positive solutions to the following nonlocal degenerate parabolic equation

     

Life span of solutions with large initial data for a semilinear parabolic system

We investigate the initial-boundary value problem

     

Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws

We consider a system of heat equations u_t=Δu and v_t=Δv in Ω×(0,T) completely coupled by nonlinear boundary conditions

We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow-up only occurs on ∂Ω with

for p,q>0, 0≤α<1 and 0≤β<p.     

Existence and nonexistence results for higher-order semilinear evolution inequalities with critical potential

We prove nonexistence results for higher-order semilinear evolution equations and inequalities of the form

     

Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction

We study radially symmetric solutions of a class of chemotaxis systems generalizing the prototype

     

Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source

In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations

in Ω×(0,T) with initial and Dirichlet boundary conditions, where Ω is a bounded domain in . Under suitable assumptions on the functions g_i(), , the initial data and the parameters in the equations, we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property.     

Life span of solutions with large initial data for a superlinear heat equation

We investigate the initial-boundary problem

     

On the Fujita exponent for a semilinear heat equation with a potential term

We consider the existence and nonexistence of positive global solutions for the Cauchy problem,

     

Higher order equations related to thin films: Blow-up and global existence, the influence of the initial data

We are interested in the following class of equations:

     

Asymptotic behavior of a degenerate nonlocal parabolic equation

In this paper, we consider the asymptotic behavior for the degenerate nonlocal parabolic equation

     

Blow-up and global existence to a degenerate reaction-diffusion equation with nonlinear memory

In this paper, we consider a degenerate reaction-diffusion equation

     

Blow-up with logarithmic nonlinearities

We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition,

     

Blow-up and global existence for a nonlocal degenerate parabolic system

This paper investigates the blow-up and global existence of nonnegative solutions of the system

     

The asymptotic critical wave speed in a family of scalar reaction-diffusion equations

We study traveling wave solutions for the class of scalar reaction-diffusion equations

     

Global existence and blow-up problems for reaction diffusion model with multiple nonlinearities

In this paper, we study the following reaction diffusion model,

     

Classification of blow-up with nonlinear diffusion and localized reaction

We study the behaviour of nonnegative solutions of the reaction-diffusion equation

     

Critical exponents for a fast diffusive polytropic filtration equation with nonlinear boundary flux

In this paper, we deal with a fast diffusive polytropic filtration equation

     

Global existence and blow-up solutions for doubly degenerate parabolic system with nonlocal source

This paper deals with the following nonlocal doubly degenerate parabolic system

     

On blow-up results for solutions of inhomogeneous evolution equations and inequalities

The main purpose of this work is to obtain blow-up results for solutions of the inequality

     

The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source

The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form