Extinction for a quasilinear heat equation with absorption II. A dynamical systems approach

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

DOI:https://doi.org/10.1080/03605309408821047· OSTI ID:62426

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

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

In this paper we continue the study begun of the asymptotic behaviour near extinction for nonnegative solutions of the quasilinear parabolic equation (0.1) u{sub t} = div(u{sup {sigma}}{del}u) - u{sup 1-{sigma}}, posed in Q{sub T} = [(x,t) : x {element_of} R{sup N}, 0 < t < T], where {sigma} {element_of} (0,1) and T > 0 is the extinction time, i.e. the time at which the solution vanishes identically. We assume that the solution takes initial data (0.2) u(x,0) = u{sub 0}(x) {ge} 0, x {element_of} R{sup N}, u{sub 0} {ne} 0 and u{sub 0} is integrable. The equation appears for instance as a model for nonlinear heat propagation with absorption. Notice that it is degenerate parabolic, since the thermal conductivity K = u{sup {sigma}} is zero for u = 0. It is known that this problem admits a unique weak solution that vanishes after a finite time T > 0. 13 refs.

• Sponsoring Organization: USDOE
• OSTI ID: 62426
• Journal Information: Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 7-8 Vol. 19; ISSN 0360-5302; ISSN CPDIDZ
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
ABSORPTION
CAUCHY PROBLEM
HAMILTON-JACOBI EQUATIONS
HEAT TRANSFER
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
THERMAL CONDUCTIVITY