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)
Nonlocal boundary-value problems for abstract parabolic equations: well-posedness in Bochner spaces. (English) Zbl 1117.65077
The author consider an abstract parabolic equation v ' (t)+Av(t)=f(t) where the initial condition is replaced by the nonlocal condition v(0)=v(λ)+μ. All variables and constants takes values in a Hilbert space E and A is a linear and possible unbounded operator on this space. Under the assumption that the operator -A generates an analytic semigroup {exp(-At)} t0 with exponential decay, it is shown that the solutions to the nonlocal parabolic equation satify a coercivity estimate in terms of f and μ with the implication that the problem is well-posed. In addition, first and second order difference schemes are given and so called almost coercive inequalities are established for these (the multiplier in the inequality contains the factor min{1/τ,|lnA EE |}, where τ is the time step).
MSC:
65J10Equations with linear operators (numerical methods)
65M06Finite difference methods (IVP of PDE)
65L05Initial value problems for ODE (numerical methods)
47D06One-parameter semigroups and linear evolution equations
34G10Linear ODE in abstract spaces
35K90Abstract parabolic equations