A nonlinear parabolic equation backward in time: Regularization with new error estimates

Consider a nonlinear backward parabolic problem in the form

     

Stability of parabolic problems with nonlinear Wentzell boundary conditions

Of concern is the nonlinear uniformly parabolic problem

     

Stability estimates for parabolic problems with Wentzell boundary conditions

Of concern is the uniformly parabolic problem

     

On a backward Cauchy problem associated with continuous spectrum operator

The nonlinear backward Cauchy problem

u_t+Au(t)=f(u(t)),u(T)=φ,     

The nonlinear Schroedinger equation: Solitons dynamics

In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h→0.We prove that under suitable assumptions, the soliton approximately follows the dynamics of a point particle, namely, the motion of its barycenterqh(t) satisfies the equation

     

Semilinear reaction-diffusion systems of several components

The homogeneous Dirichlet boundary value problem

     

Nonexistence of type II blowup solution for a semilinear heat equation

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

     

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

     

Growup of solutions for a semilinear heat equation with supercritical nonlinearity

We consider a Cauchy problem for a semilinear heat equation

(P)     

Various behaviors of solutions for a semilinear heat equation after blowup

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

(P)     

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)     

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,

     

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

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

     

The heat equation with nonlinear generalized Robin boundary conditions

Let Ω⊂RN be a bounded domain and let μ be an admissible measure on ∂Ω. We show in the first part that if Ω has the H¹-extension property, then a realization of the Laplace operator with generalized nonlinear Robin boundary conditions, formally given by on ∂Ω, generates a strongly continuous nonlinear submarkovian semigroup SB=(SB(t))_t?0 on L²(Ω). We also obtain that this semigroup is ultracontractive in the sense that for every u,v∈Lp(Ω), p?2 and every t>0, one has

     

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

     

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)     

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

     

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)