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Titolo:
Geometry of unbounded domains, Poincare inequalities and stability in semilinear parabolic equations
Autore:
Souplet, P;
Indirizzi:
UnivF-9343013, Inst Galilee, CNRS, UMR 7539,Lab Anal Geometrie & Applicat,Univ Paris 13 Villetaneuse France F-93430 Lab Anal Geometrie & Applicat,
Titolo Testata:
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
fascicolo: 5-6, volume: 24, anno: 1999,
pagine: 951 - 973
SICI:
0360-5302(1999)24:5-6<951:GOUDPI>2.0.ZU;2-K
Fonte:
ISI
Lingua:
ENG
Soggetto:
REACTION-DIFFUSION EQUATIONS; TIME BLOW-UP; GRADIENT TERM; HEAT-EQUATION; CRITICAL EXPONENT; GLOBAL EXISTENCE; CAUCHY-PROBLEM; NONEXISTENCE;
Keywords:
semilinear parabolic equations; global existence; stability; blow-up; inradius; Poincare inequality;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
43
Recensione:
Indirizzi per estratti:
Indirizzo: Souplet, P UnivF-9343013, Inst Galilee, CNRS, UMR 7539,Lab Anal Geometrie & Applicat, Univ Paris 13 Villetaneuse France F-93430 ometrie & Applicat,
Citazione:
P. Souplet, "Geometry of unbounded domains, Poincare inequalities and stability in semilinear parabolic equations", COMM PART D, 24(5-6), 1999, pp. 951-973

Abstract

We investigate the close relations existing between certain ge ometric properties of domains Omega of R-N, the validity of PoincarC inequalities in Omega, and the behavior of solutions of semilinear parabolic equations. For the equation u(t) - Delta u = \u\(p-1) u, p > 1, we Obtain a purely geometric, necessary and sufficient condition on Omega, for the 0 solution tobe asymptotically (and exponentially) stable in L-r(Omega), 1 < r < infinity, when r is supercritical (r > N (p - 1)/2). The condition is that tho inradius of Omega be finite. The result is different for 1 critical. For the equation u(t) - Delta u = u(p) - mu\del u\(q), q greater than or equal to p > 1, mu > 0, we prove that the finiteness of the inradius is a necessary and sufficient condition for global existence and boundedness of all nonnegative solutions. AMS CLASSIFICATION: 35K60, 35B35, 35B60, 46E35.

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Documento generato il 31/03/20 alle ore 22:28:31