Uniqueness of determination of the unknown source term in some multidimensional parabolic equations
DOI:
https://doi.org/10.4067/S0716-09172004000200001Keywords:
Multidimensional parabolic equations, boundary measurements, interior measurements, one-point measurements, ecuaciones parabólicas multidimensionales, medidas de acotación, medidas interiores, medidas de un punto.Abstract
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 x? ? ?, i.e. u(x?, .) on [0, T ]; or a one-point boundary measurement, i.e. u(x??, .) on [0, T ] with x?? ? ??.References
[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, (1998).
[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, pp. 1051-1053, (1992).
[6] P. DuChateau, Monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation, Siam J. Appl. Math. 41, pp. 310-323, (1981).
[7] P. DuChateau and W. Rundell, Unicity in an inverse problem for an unknown reaction term in a reaction-diffusion equation, J. Diff. Equations 59, pp. 155-164, (1985).
[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. 143-191, (1993).
[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).
[2] J. R. Cannon and P. DuChateau, Structural identification of an unknown source term in a heat equation, Inverse problems 14, pp. 535-551, (1998).
[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, pp. 1051-1053, (1992).
[6] P. DuChateau, Monotonicity and uniqueness results in identifying an unknown coefficient in a nonlinear diffusion equation, Siam J. Appl. Math. 41, pp. 310-323, (1981).
[7] P. DuChateau and W. Rundell, Unicity in an inverse problem for an unknown reaction term in a reaction-diffusion equation, J. Diff. Equations 59, pp. 155-164, (1985).
[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. 143-191, (1993).
[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).
Published
2017-05-22
How to Cite
[1]
A. Zhegal, “Uniqueness of determination of the unknown source term in some multidimensional parabolic equations”, Proyecciones (Antofagasta, On line), vol. 23, no. 2, pp. 81-90, May 2017.
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