Abstract and Applied Analysis

Abstract and Applied Analysis / 2006 / Article

Open Access

Volume 2006 |Article ID 061203 | https://doi.org/10.1155/AAA/2006/61203

Bui An Ton, "On the exact controllability of a nonlinear stochastic heat equation", Abstract and Applied Analysis, vol. 2006, Article ID 061203, 12 pages, 2006. https://doi.org/10.1155/AAA/2006/61203

On the exact controllability of a nonlinear stochastic heat equation

Received12 Dec 2004
Accepted20 Jan 2005
Published01 Mar 2006

Abstract

The exact controllability of a nonlinear stochastic heat equation with null Dirichlet boundary conditions, nonzero initial and target values, and an interior control is established.

References

  1. B. A. Ton, “Exact controllability for a semilinear wave equation with both interior and boundary controls,” to appear in Abstract and Applied Analysis, 2005. View at: Google Scholar | Zentralblatt MATH | MathSciNet
  2. A. Bensoussan and R. Temam, “Équations stochastiques du type Navier-Stokes,” Journal of Functional Analysis, vol. 13, no. 2, pp. 195–222, 1973 (French). View at: Google Scholar | Zentralblatt MATH | MathSciNet
  3. C. Fabre, J.-P. Puel, and E. Zuazua, “Contrôlabilité approchée de l'équation de la chaleur semi-linéaire [Approximate controllability for the semilinear heat equation],” Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, vol. 315, no. 7, pp. 807–812, 1992 (French). View at: Google Scholar | Zentralblatt MATH | MathSciNet
  4. G. Lebeau and L. Robbiano, “Contrôle exact de l'équation de la chaleur [Exact control of the heat equation],” Communications in Partial Differential Equations, vol. 20, no. 1-2, pp. 335–356, 1995 (French). View at: Google Scholar | Zentralblatt MATH | MathSciNet
  5. D. L. Russell, “A unified boundary controllability theory for hyperbolic and parabolic partial differential equations,” SIAM Studies in Applied Mathematics, vol. 52, no. 3, pp. 189–211, 1973. View at: Google Scholar
  6. E. Zuazua, “Exact boundary controllability for the semilinear wave equation,” in Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar, Vol. X (Paris, 1987–1988), vol. 220 of Pitman Res. Notes Math. Ser., pp. 357–391, Longman Science Technology, Harlow, 1991. View at: Google Scholar | Zentralblatt MATH | MathSciNet

Copyright © 2006 Bui An Ton. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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