zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Life span of positive solutions for a semilinear heat equation with general non-decaying initial data. (English) Zbl 1215.35091
Summary: We prove upper bounds on the life span of positive solutions for a semilinear heat equation. For non-decaying initial data, it is well known that the solutions blow up in finite time. We give two types of estimates of the life span in terms of the limiting values of the initial data in space.

35K58Semilinear parabolic equations
35B44Blow-up (PDE)
35K15Second order parabolic equations, initial value problems
Full Text: DOI
[1] Giga, Y.; Umeda, N.: On blow-up at space infinity for semilinear heat equations, J. math. Anal. appl. 316, 538-555 (2006) · Zbl 1106.35029 · doi:10.1016/j.jmaa.2005.05.007
[2] Giga, Y.; Umeda, N.: Blow-up directions at space infinity for semilinear heat equations, Bol. soc. Parana. mat. 23, 9-28 (2005) · Zbl 1173.35531
[3] Gui, C.; Wang, X.: Life spans of solutions of the Cauchy problem for a semilinear heat equation, J. differential equations 115, 166-172 (1995) · Zbl 0813.35034 · doi:10.1006/jdeq.1995.1010
[4] Lee, T. Y.; Ni, W. M.: Global existence, large time behavior and life span of solutions of a semilinear parabolic Cauchy problem, Trans. amer. Math. soc. 333, 365-378 (1992) · Zbl 0785.35011 · doi:10.2307/2154114
[5] Mochizuki, K.; Suzuki, R.: Blow-up sets and asymptotic behavior of interfaces for quasilinear degenerate parabolic equations in RN, J. math. Soc. Japan 44, 485-504 (1992) · Zbl 0805.35065 · doi:10.2969/jmsj/04430485
[6] Seki, Y.: On directional blow-up for quasilinear parabolic equations with fast diffusion, J. math. Anal. appl. 338, 572-587 (2008) · Zbl 1144.35030 · doi:10.1016/j.jmaa.2007.05.033
[7] Seki, Y.; Umeda, N.; Suzuki, R.: Blow-up directions for quasilinear parabolic equations, Proc. roy. Soc. Edinburgh sect. A 138, 379-405 (2008) · Zbl 1167.35393 · doi:10.1017/S0308210506000801
[8] Yamaguchi, M.; Yamauchi, Y.: Life span of positive solutions for a semilinear heat equation with non-decaying initial data, Differential integral equations 23, 1151-1157 (2010) · Zbl 1240.35218