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)
Approximate controllability of a parabolic equation with memory. (English) Zbl 1238.93018
Summary: We study the approximate controllability of a parabolic equation with memory $y_t + y_{xx} + \int^t_0 y(x,s)ds = 0$ by boundary control. The proof relies on the explicit solution of the corresponding homogeneous initial boundary value problem and a duality method.

93C20Control systems governed by PDE
35R09Integro-partial differential equations
Full Text: DOI
[1] Volterra, V.: Theory of functionals, (1930) · Zbl 55.0814.01
[2] Yamada, Y.: On a certain class of semilinear Volterra diffusion equations, J. math. Anal. appl. 88, 433-457 (1982) · Zbl 0515.45012 · doi:10.1016/0022-247X(82)90205-0
[3] Yamada, Y.: Asymptotic stability for some systems of semilinear Volterra diffusion equations, J. differ. Equ. 52, 295-326 (1984) · Zbl 0543.35053 · doi:10.1016/0022-0396(84)90165-7
[4] Zhang, N. Y.: On fully discrete Galerkin approximations for partial integrodifferential equations of parabolic type, Math. comp. 60, 133-166 (1993) · Zbl 0795.65098 · doi:10.2307/2153159
[5] Blanchard, D.; Ghidouche, H.: A nonlinear system for irreversible phase changes, European J. Appl. math. 1, 91-100 (1990) · Zbl 0713.35045 · doi:10.1017/S0956792500000073
[6] Barbu, V.; Iannelli, M.: Controllability of the heat equation with memory, Differ. integral equ. 13, 1393-1412 (2000) · Zbl 0990.93008
[7] Fu, X.; Yong, J.; Zhang, X.: Controllability and observability of a heat equation with hyperbolic memory kernel, J. differ. Equ. 247, 2395-2439 (2009) · Zbl 1187.35265 · doi:10.1016/j.jde.2009.07.026
[8] Sakthivel, K.; Balachandran, K.; Nagaraj, B. R.: On a class of non-linear parabolic control systems with memory effects, Internat. J. Control 81, 764-777 (2008) · Zbl 1152.93312 · doi:10.1080/00207170701447114
[9] Lavanya, R.; Balachandran, K.: Null controllability of nonlinear heat equations with memory effects, Nonlinear anal. Hybrid syst. 3, 163-175 (2009) · Zbl 1166.93004 · doi:10.1016/j.nahs.2008.12.003
[10] Prüss, J.: Evolutionary integral equations and applications, (1993) · Zbl 0784.45006
[11] Rosier, L.; Rouchon, P.: On the controllability of a wave equation with structural damping, Int. J. Tomogr. stat. 5, 79-84 (2007)