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

The purpose of this book is to present typical methods (including rescaling methods) for the
examination of the behavior of solutions of nonlinear partial di? erential equations of di …

We study in the present article the Kardar–Parisi–Zhang (KPZ) equation ∂ _t h (t, x)= ν Δ h
(t, x)+ λ| ∇ h (t, x)|^ 2+ D\, η (t, x),\qquad (t, x) ∈ R _+ * R^ d∂ th (t, x)= ν Δ h (t, x)+ λ|∇ h (t …

We consider the viscous Hamilton-Jacobi (VHJ) equation ut-Δ u=|∇ u| p+ h (x). For the
Dirichlet problem with p> 2, it is known that gradient blow-up may occur in finite time (on the …

GLOBAL SOLUTIONS FOR A NONLINEAR INTEGRAL EQUATION WITH A GENERALIZED
HEAT KERNEL Kazuhiro Ishige Tatsuki Kawakami Kanako Kobaya Page 1 DISCRETE AND …

This paper is concerned with a nonlinear integral equation $$(P)\qquad u (x, t)=\int_ {{\bf R}^
N} G (xy, t)\varphi (y) dy+\int_0^ t\int_ {{\bf R}^ N} G (xy, ts) f (y, s: u) dyds,\quad $$ where …

Nonlinear and nonlocal evolution equations of the form $ u_t=\mathcal {L} u\pm|\nabla u|^ q
$, where $\mathcal {L} $ is a pseudodifferential operator representing the infinitesimal …

The nonlinear partial differential equation in the title is typified mathematically as a viscous
Hamilton–Jacobi equation. It arises in the study of the growth of surfaces, and in that context …

We study the long-time behavior of the unique viscosity solution u of the viscous Hamilton–
Jacobi equation ut− Δu+| Du| m= f in Ω×(0,+∞) with inhomogeneous Dirichlet boundary …

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 …