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)
Nonadiabatic plane laminar flames and their singular limits. (English) Zbl 0714.34042

New results concerning nonadiabatic travelling waves and their singular limits are presented. By means of standard combustion approximations the model reduces to a two-point boundary value problem on the real line with an eigenvalue:

-u '' +cu ' =f(u)v n -λg(u),-v '' +cv ' =-f(u)v n ,u(-)=0,v(-)=1,u(+)=0,v ' (+)=0·

Here u denotes the reduced temperature, v the reactant mass fraction, c the reduced mass flux, f the reduced source term, λ the reduced heat loss rate in the hot gases, and g the reduced heat loss rate function.

The natural problem would be to find a nontrivial solution (u,v,c), with (u,v)(0,1) and c>0. Existence of a solution is achieved by first considering the problem in a bounded domain and then by taking an infinite domain limit. The author proves strong convergence of the nonadiabatic travelling wave to singular limit free-boundary solutions with discontinuous derivatives.

Reviewer: L.M.Berkovich
MSC:
34B15Nonlinear boundary value problems for ODE
34E20Asymptotic singular perturbations, turning point theory, WKB methods (ODE)
34L05General spectral theory for OD operators
80A25Combustion, interior ballistics
34B10Nonlocal and multipoint boundary value problems for ODE