TY - JOUR

T1 - Asymptotic analysis and estimates of blow-up time for the radial symmetric semilinear heat equation in the open-spectrum case

AU - Kavallaris, N. I.

AU - Lacey, A. A.

AU - Nikolopoulos, C. V.

AU - Tzanetis, D. E.

PY - 2007/9/10

Y1 - 2007/9/10

N2 - We estimate the blow-up time for the reaction diffusion equation u t = ?u+?f(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here ?>?*, where ?* is the 'extremal' (critical) value for ?, such that there exists an 'extremal' weak but not a classical steady-state solution at ? = ?* with ||w(?)||8 ? infin; as 0<? ? ?*-. Estimates of the blow-up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s) = es, for ? - ?* «1, regarding the form of the solution during blow-up and an asymptotic estimate of blow-up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.

AB - We estimate the blow-up time for the reaction diffusion equation u t = ?u+?f(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here ?>?*, where ?* is the 'extremal' (critical) value for ?, such that there exists an 'extremal' weak but not a classical steady-state solution at ? = ?* with ||w(?)||8 ? infin; as 0<? ? ?*-. Estimates of the blow-up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s) = es, for ? - ?* «1, regarding the form of the solution during blow-up and an asymptotic estimate of blow-up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.

KW - Blow-up time estimates

KW - Boundary-layer theory

KW - Reaction diffusion equation

UR - http://www.scopus.com/inward/record.url?scp=34547623419&partnerID=8YFLogxK

U2 - 10.1002/mma.854

DO - 10.1002/mma.854

M3 - Article

VL - 30

SP - 1507

EP - 1526

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 13

ER -