Uniqueness of determination of the unknown source term in some multidimensional parabolic equations

• Zhegal, A. ^[1]
  1. [1] Cadi Ayyad University

     Cadi Ayyad University

     Marrakech-Medina, Marruecos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 23, Nº. 2, 2004, págs. 81-90
• Idioma: inglés
• DOI: 10.4067/S0716-09172004000200001
• Enlaces
  • Texto completo
• Resumen

  • The purpose of this paper is to identify the unknown source term in a multidimensional parabolic equation by means of a one-point interior  measurement of the solution at x₀ ∈ Ω, i.e. u(x₀, .) on [0, T ]; or a one-point boundary measurement, i.e. u(x̅₀, .) on [0, T ] with x̅₀ ∈ ∂Ω.

• Referencias bibliográficas
  • Citas [1] J. R. Cannon and P. DuChateau, An inverse problem for a nonlinear diffusion equation, SIAM J. Appl. Math. 39, pp. 272-289, (1980).
  • [2] J. R. Cannon and P. DuChateau, Structural identification of an unknown source term in a heat equation, Inverse problems 14, pp. 535-551,...
  • [3] M. Choulli, Identifiability of an unknown coefficient in a nonlinear diffusion equation, Quart. Appl. Math. 47, pp. 9-16, (1989).
  • [4] M. Choulli, On the determination of an unknown boundary function in a parabolic equation, Inverse problems 15, pp. 659-667, (1999).
  • [5] M. Choulli and A. Zeghal, Un résultat d’unicité pour un probleme inverse parabolique semi-linéaire, C. R. Acad. Sci. Paris Sér. I 315,...
  • [6] P. DuChateau, Monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation, Siam J. Appl....
  • [7] P. DuChateau and W. Rundell, Unicity in an inverse problem for an unknown reaction term in a reaction-diffusion equation, J. Diff. Equations...
  • [8] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, (1964).
  • [9] V. Isakov, Uniqueness and stability in multi-dimensional inverse problems, Inverse Problems 9, pp. 579-621, (1993).
  • [10] O. A. Ladyzhenskaja, V. A. Solonnikov and N. N. Uralceva, Linear and Quasi-linear Equations of Parabolic Type, Providence, RI, (1968).
  • [11] S. Nakagiri, Review of Japanese work of the last ten years on identifiability in distributed parameter systems, Inverse Problems 9, pp....
  • [12] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Springer-Verlag, New York, (1984).
  • [13] M. Renardy and R. C. Rogers An Introduction to Partial Differential Equations, Springer-Verlag, New York, (1993).