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Titolo:
The critical exponent of doubly singular parabolic equations
Autore:
Liu, XF; Wang, MX;
Indirizzi:
SE Univ, Dept Appl Math, Nanjing 210018, Peoples R China SE Univ NanjingPeoples R China 210018 , Nanjing 210018, Peoples R China
Titolo Testata:
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
fascicolo: 1, volume: 257, anno: 2001,
pagine: 170 - 188
SICI:
0022-247X(20010501)257:1<170:TCEODS>2.0.ZU;2-1
Fonte:
ISI
Lingua:
ENG
Soggetto:
BLOW-UP; THEOREMS; SYSTEMS;
Keywords:
doubly singular parabolic equation; critical exponent; blow up;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
24
Recensione:
Indirizzi per estratti:
Indirizzo: Liu, XF SE Univ, Dept Appl Math, Nanjing 210018, Peoples R China SE Univ Nanjing Peoples R China 210018 g 210018, Peoples R China
Citazione:
X.F. Liu e M.X. Wang, "The critical exponent of doubly singular parabolic equations", J MATH ANAL, 257(1), 2001, pp. 170-188

## Abstract

In this paper we study the Cauchy problem of doubly singular parabolic equations u(t) = div(\delu\(sigma) delu(m)) + t(s)\x\(0)u(p) with non-negativeinitial data. Here -1 < sigma less than or equal to 0. m > max{0, 1 - sigma - (sigma + 2)/N} satisfying 0 < sigma + m less than or equal to 1, p > 1,and s greater than or equal to 0. We prove that if theta > max{-(sigma + 2), (1 + s)[N(1 - sigma - m) - (sigma + 2)]}, then p(c) = (sigma + m) + (sigma + m - 1)s + [(sigma + 2)(1 + s) + theta]/N > 1 is the critical exponent;i.e, if 1 < p less than or equal to p(c) then every non-trivial solution blows up in finite time. But for I? s p, a positive global solution exists. (C) 2001 Academic Press.

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Documento generato il 29/03/20 alle ore 12:12:58