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)
Interior controllability of a broad class of reaction diffusion equations. (English) Zbl 1206.93017
Summary: We prove the interior approximate controllability of the following broad class of reaction diffusion equation in the Hilbert spaces Z=L 2 (Ω) given by z ' =-Az+1 ω u(t), t[0,τ], where Ω is a domain in n , ω is an open nonempty subset of Ω, 1 ω denotes the characteristic function of the set ω, the distributed control uL(0,t 1 ;L 2 (Ω)) and A:D(A) is an unbounded linear operator with the following spectral decomposition: Az= j=1 λ j k=1 γ j z,ϕ j,k ϕ j,k . The eigenvalues 0<λ 1 <λ 2 <<λ n of A have finite multiplicity γ j equal to the dimension of the corresponding eigenspace, and {ϕ j,k } is a complete orthonormal set of eigenvectors of A. The operator -A generates a strongly continuous semigroup {T(t)} given by T(t)z= j=1 e -λ j t k=1 γ j z,ϕ j,k ϕ j,k . Our result can be applied to the nD heat equation, the Ornstein-Uhlenbeck equation, the Laguerre equation, and the Jacobi equation.
MSC:
93B05Controllability
60J65Brownian motion
80A20Heat and mass transfer, heat flow
35K57Reaction-diffusion equations