Blowup rate of solutions for a semilinear heat equation with the Neumann boundary condition

Let p>1 and Ω be a smoothly bounded domain in . This paper is concerned with a Cauchy-Neumann problem

     

Parabolic approach to nonlinear elliptic eigenvalue problems

We consider the asymptotic profiles of the nonlinear parabolic flows ut=Δum to show the geometric properties of the following elliptic nonlinear eigenvalue problems:

     

Semilinear reaction-diffusion systems of several components

The homogeneous Dirichlet boundary value problem

     

On the Cauchy problem for the fast diffusion equation

For , the author studies the existence of a kind of weak solution to the Cauchy problem

     

Initial blow-up of solutions of semilinear parabolic inequalities

We study classical nonnegative solutions u(x,t) of the semilinear parabolic inequalities

     

Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents

We describe special asymptotic structures of solutions of the semilinear heat equation

     

Blow up rate for a porous medium equation with power nonlinearity

The present paper is concerned with the blow up rate of a solution to the following Cauchy problem

     

Blow-up phenomena for a doubly degenerate equation with positive initial energy

In this paper, an initial boundary value problem related to the equation

     

On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation, I: Local oscillatory properties

As a key example, the sixth-order doubly degenerate parabolic equation from thin film theory,

     

Convergence to steady states in a viscous Hamilton-Jacobi equation with degenerate diffusion

This paper deals with weak solutions of the one-dimensional viscous Hamilton-Jacobi equation

     

On the Cauchy problem for a reaction-diffusion equation with a singular nonlinearity

We consider the following Cauchy problem with a singular nonlinearity

(P)

     

Life span and a new critical exponent for a degenerate parabolic equation

In this paper, we consider the positive solution of the Cauchy problem for the equation

     

Large-time geometric properties of solutions of the evolution p-Laplacian equation

We establish the behavior of the solutions of the degenerate parabolic equation

     

A global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure

In this paper we investigate the pseudoparabolic equation

     

Stability of parabolic problems with nonlinear Wentzell boundary conditions

Of concern is the nonlinear uniformly parabolic problem

     

Optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a Hardy potential

We deal with the following parabolic problem

     

A sufficient condition for type I blowup in a parabolic-elliptic system

This paper is concerned with blowup of positive solutions to a Cauchy problem for a parabolic-elliptic system