Nonexistence of type II blowup solution for a semilinear heat equation

A solution u of a Cauchy problem for a semilinear heat equation

     

Semilinear reaction-diffusion systems of several components

The homogeneous Dirichlet boundary value problem

     

Growup of solutions for a semilinear heat equation with supercritical nonlinearity

We consider a Cauchy problem for a semilinear heat equation

(P)     

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

     

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

     

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,

     

Blowup behavior of solutions for a semilinear heat equation with supercritical nonlinearity

This paper is concerned with blowup phenomena of solutions for the Cauchy and the Cauchy-Dirichlet problem of

(P)     

Multiple blowup of solutions for a semilinear heat equation II

The present paper is concerned with a Cauchy problem for a semilinear heat equation

(P)     

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

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

     

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

     

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

     

The porous medium equation in a two-component domain

We consider a system of two porous medium equations defined on two different components of the real line, which are connected by the nonlinear contact condition

     

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

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

     

Homogenization limit of a parabolic equation with nonlinear boundary conditions

Consider the parabolic equation

(E)     

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

     

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

     

Stability of parabolic problems with nonlinear Wentzell boundary conditions

Of concern is the nonlinear uniformly parabolic 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:

     

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

     

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