We consider viscous Hamilton–Jacobi equations of the form [Formula: see text] where a∈ R,
a≠ 0 and p⩾ 1. We provide an extensive investigation of the local Cauchy problem for (VHJ) …

With qa positive real number, the nonlinear partial differential equation in the title of the
paper arises in the study of the growth of surfaces. In that context it is known as the …

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 …

The purpose of the paper is to study properties of solutions of the Cauchy problem for the
equation u_t-Δ u+| ∇ u|^ q= 0 under the assumption (n+ 2)/(n+ 1)< q< 2. General selfsimilar …

Decay of mass for a semilinear parabolic equation Page 1 COMMUN. IN PARTIAL
DIFFERENTIAL EQUATIONS, 24(5&6), 869-88 1 (1 999) DECAY OF MASS FOR A SEMILINEAR …

We investigate thc close relations existing between certain geometric properties of domains
Ω of RN, the validity of Poincark inequalities in Ω, and the behavior of solutions of semilinear …

We study qualitative properties of non-negative solutions to the Cauchy problem for the fast
diffusion equation with gradient absorption where N⩾ 1, p∈(1, 2), and q> 0. Based on …

Extinction in finite time and non-compactness of the support are investigated for non-
negative classical solutions to the Cauchy problem ut−∆ u+|∇ u| p= 0 when p∈(0, 1). The …

We consider non-negative and integrable classical solutions to the Cauchy problem $ u_t-
\Delta u+\vert\nabla u\vert^ p= 0$ when $ p\in (0,+\infty) $. For $ p\in (0, N/(N+ 1)) $ we prove …

Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic
equation with an absorption term depending solely on the gradient are shown, providing …