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)
The role of critical exponents in blow-up theorems: The sequel. (English) Zbl 0942.35025
Consider the Cauchy problem in N for the equation u t =Δu+u p , where p>1 and u0. In 1966, H. Fujita [J. Fac. Sci., Univ. Tokyo, Sect. I 13, 109-124 (1966; Zbl 0163.34002)] showed that this problem does not have global nontrivial solutions if p<p c :=1+2/N whereas both global and non-global positive solutions exist if p>p c . The exponent p c is called Fujita’s critical exponent. The authors discuss various Fujita-type results which have appeared in the literature since 1990. These results include degenerate equations, problems in unbounded domains and on manifolds, problems with inhomogeneous boundary conditions, cooperative systems of equations. Moreover, the paper contains a section with open problems.

35B33Critical exponents (PDE)
35K55Nonlinear parabolic equations
35B35Stability of solutions of PDE
35B40Asymptotic behavior of solutions of PDE