Pavol Quittner Philippe Souplet Blow-up, Global Existence and Steady States Second
Edition Page 1 Birkhäuser Advanced Texts Basler Lehrbücher Pavol Quittner Philippe …

Dissipative equations have attracted substantial attention over many years. Much progress
has been achieved in this area using a combination of both finite dimensional and infinite …

The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial
differential equation has been an area of intense re search activity in mathematics. Some …

We consider nonlinear parabolic equations with gradient-dependent nonlinearities, of the
form u_t-Δu=F(u,∇u). These equations are studied on smoothly bounded domains of …

L00-blow-up of solutions of semilinear parabolic equations has received considerable
interest. Several major problems like sufficient conditions for blow-up, the form of the blow …

Abstract Consider the diffusive Hamilton-Jacobi equation ut= Δ u+|∇ u| p, p> 2, on a
bounded domain Ω with zero-Dirichlet boundary conditions, which arises in the KPZ model …

This paper is concerned with weak solutions of the degenerate diffusive Hamilton–Jacobi
equation with Dirichlet boundary conditions in a bounded domain Ω⊂ RN, where p> 2 and …

Abstract Consider the diffusive Hamilton–Jacobi equation u_t-Δ u=| ∇ u|^ p+ h (x)\in Ω * (0,
T) ut-Δ u=|∇ u| p+ h (x) in Ω×(0, T) with Dirichlet conditions, which arises in stochastic …

The present paper is concerned with the Bernstein-Nagumo's condition for nonlinear and
quasilinear parabolic equations. We show that Bernstein-Nagumo's condition can be …

We establish the existence of locally positive weak solutions to the homogeneous Dirichlet
problem for u_t=uΔu+u\int_Ω|∇u|^2 in bounded domains Ω⊂R^n which arises in game …