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 class of integro-differential variational inequalities with applications to viscoelastic contact. (English) Zbl 1080.47052
Summary: We consider a class of abstract evolutionary variational inequalities arising in the study of frictional contact problems for linear viscoelastic materials with long-term memory. First, we prove an abstract existence and uniqueness result, by using arguments of evolutionary variational inequalities and Banach’s fixed point theorem. Next, we study the dependence of the solution on the memory term and derive a convergence result. Then, we consider a contact problem to which the abstract results apply. The problem models a quasistatic process, the contact is bilateral and the friction is modeled with Tresca’s law. We prove the existence of a unique weak solution to the model and we provide the mechanical interpretation of the corresponding convergence result. Finally, we extend these results to the study of a number of quasistatic frictional problems for linear viscoelastic materials with long-term memory.

47N60Applications of operator theory in biology and other sciences
47J20Inequalities involving nonlinear operators
47J35Nonlinear evolution equations
74D99Materials of strain-rate type and history type, other materials with memory
74M10Friction (solid mechanics)
74M15Contact (solid mechanics)