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)
A concept of solution and numerical experiments for forward-backward diffusion equations. (English) Zbl 1105.35007
The authors study the gradient flow associated with the functional F φ (u):=1 2 I φ(u x )dx, where φ is non convex, and with its singular perturbation F φ x (u):=1 2 I (ε 2 (u xx ) 2 +φ(u x ))dx. With the support of numerical simulations, various aspects of the global dynamics of solutions u ε of the singularly perturbed equation u t =-ε 2 u xxxx +1 2φ '' (u x )u xx for small values of ε>0 are discussed. Their analysis leads to a reinterpretation of the unperturbed equation u tt =1 2(φ ' (u x )) x , and to a well defined notion of a solution. Examine the conjecture that this solution coincides with the limit of u ε as ε0 + is given.
35B25Singular perturbations (PDE)
35K55Nonlinear parabolic equations
34E13Multiple scale methods (ODE)
49L25Viscosity solutions (infinite-dimensional problems)
35A15Variational methods (PDE)