Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
AS Kalashnikov - Russian Mathematical Surveys, 1987 - iopscience.iop.org
Abstract CONTENTS Introduction Chapter I. Existence and uniqueness of generalized
solutions of the Cauchy problem and of initial boundary-value problems § 1.1. Theorems of …
solutions of the Cauchy problem and of initial boundary-value problems § 1.1. Theorems of …
On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium
We prove the uniqueness (as well as the existence and regularity) of solutions of the Cauchy
problem and of the first and mixed boundary value problems for the equation ut= φ (u) xx+ b …
problem and of the first and mixed boundary value problems for the equation ut= φ (u) xx+ b …
Some existence and nonexistence theorems for solutions of degenerate parabolic equations
The initial and boundary value problem for the degenerate parabolic equation vt= Δ (ϑ (v))+
F (v) in the cylinder Ωצ 0,∞), Ω⊂ R n bounded, for a certain class of point functions ϑ …
F (v) in the cylinder Ωצ 0,∞), Ω⊂ R n bounded, for a certain class of point functions ϑ …
Thermal waves in an absorbing and convecting medium
P Rosenau, S Kamin - Physica D: Nonlinear Phenomena, 1983 - Elsevier
The quasi-linear parabolic equation∂ tu= a∂ xx u α+ b∂ xu β− cu γ exhibits a wide variety
of wave phenomena, some of which are studied in this work; and some solvable cases are …
of wave phenomena, some of which are studied in this work; and some solvable cases are …
On the propagation properties of a nonlinear degenerate parabolic equation
This paper studies the Cauchy problem for the equation with initial condition: for x BR: Here
m is a constant, 0< m< m. For m= 1,(0.1) is the classical heat equation. If m# 1,(0.1) appears …
m is a constant, 0< m< m. For m= 1,(0.1) is the classical heat equation. If m# 1,(0.1) appears …
The characterization of reaction-convection-diffusion processes by travelling waves
BH Gilding, R Kersner - Journal of differential equations, 1996 - Elsevier
It has long been known that the heat equation displays infinite speed of propagation. This is
to say that if the initial data are nonnegative and have nonempty compact support, the …
to say that if the initial data are nonnegative and have nonempty compact support, the …
Hausdoff measure estimates of a free boundary for a minimum problem
D Phillips - Communications in Partial Differential Equations, 1983 - Taylor & Francis
Hausdoff measure estimates of a free boundary for a minimum problem Page 1 COMM. IN
PARTIAL DIFFERENTIAL EQUATIONS, 8(13), 1409-1454 (1983) HAUSDORFF MEASURE …
PARTIAL DIFFERENTIAL EQUATIONS, 8(13), 1409-1454 (1983) HAUSDORFF MEASURE …
The one-dimensional nonlinear heat equation with absorption: Regularity of solutions and interfaces
We consider the equation u_t=(u^m)_xx-λu^n with m>1, λ>0, n\geqqm as a model for heat
diffusion with absorption. Hence we assume that u\geqq0 for x∈R, t\geqq0. We study the …
diffusion with absorption. Hence we assume that u\geqq0 for x∈R, t\geqq0. We study the …
Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption.
M Mimura, H Matano, XY Chen - 1995 - degruyter.com
Equations of this type arise in various fields of science such s fluid dynamics [35], plasma
physics [33] and mathematical ecology [29]. In a mathematical model for a heat conduction …
physics [33] and mathematical ecology [29]. In a mathematical model for a heat conduction …
[PDF][PDF] Extinction for fast diffusion equations with nonlinear sources.
Y Li, J Wu - Electronic Journal of Differential Equations (EJDE) …, 2005 - eudml.org
We establish conditions for the extinction of solutions, in finite t ime, of the fast diffusion
problem ut=∆ um+ λup, 0< m< 1, in a bounded domain of RN with N> 2. More precisely, we …
problem ut=∆ um+ λup, 0< m< 1, in a bounded domain of RN with N> 2. More precisely, we …