zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
An existence theorem for parabolic equations on N with discontinuous nonlinearity. (English) Zbl 1056.35082

The paper deals with the initial value problem

(1) t u=Δu+f(u),(2)u(x,0)=α(x),

where x N , t>0, here α is a bounded uniformly continuous function and r is bounded, measurable but generally a non-continuous one. The problem is motivated by the model of best response dynamics arising in game theory [see the first author, Ann. Oper Res. 89, 233–251 (1999; Zbl 0942.91018)]. The theorem proved by the authors claims that (1), (2) has a generalized (in the sense derived in the paper) solution. The proof is based on solving the problem (1), (2) with f replaced by f n , where (f n ) is a sequence of C functions approximating f. Then the Arzela-Ascoli theorem is applied to the corresponding sequence (u n of solutions and the uniform limit of a subsequence of (u n ) is the desired solution of (1), (2).

MSC:
35K57Reaction-diffusion equations
35K15Second order parabolic equations, initial value problems
35D05Existence of generalized solutions of PDE (MSC2000)