Extinction for a quasilinear heat equation with absorption I. Technique of intersection comparison

Journal Article · Sat Dec 31 04:00:00 EST 1994 · Communications in Partial Differential Equations

DOI:https://doi.org/10.1080/03605309408821046· OSTI ID:62425

Galaktionov, V A ^[1]; Vazquez, J L ^[2]

---

1. Keldysh Institute of Applied Mathematics, Moscow (Russian Federation)
2. Universidad Autonoma de Madrid (Spain)

A nonlinear process of heat propagation with absorption in a homogeneous isotropic medium is described. More generally, the equation for such a process takes the form u{sub t} = div(K(u){del}u) - A(u)u, where K, the thermal conductivity, and A, the absorption coefficient, are continuous and positive functions of the temperature u > 0. This equation can also be used to describe diffusion processes. Then u is a density or a concentration, and K(u) represents the diffusivity. We are interested in studying asymptotic properties of extinction phenomena. It is a field that has been only recently treated in a rigorous mathematical fashion, and this almost exclusively for one-dimensional semilinear equations, i.e. when K(u) is constant, cf. [HVe] and references therein. Several interesting properties of solutions of the one-dimensional equation with strong absorption and power nonlinearities were studied in the recent paper [CMM], but detailed asymptotic space-time behaviour near the extinction time was not considered.

• Sponsoring Organization: USDOE
• OSTI ID: 62425
• Journal Information: Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 7-8 Vol. 19; ISSN CPDIDZ; ISSN 0360-5302
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
ABSORPTION
CAUCHY PROBLEM
HEAT TRANSFER
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
QUASILINEAR PROBLEMS
THERMAL CONDUCTIVITY