Some inverse problems of identification for integrodifferential parabolic systems with a boundary memory term

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August 2015, 8(4): 749-756. doi: 10.3934/dcdss.2015.8.749

Some inverse problems of identification for integrodifferential parabolic systems with a boundary memory term

Davide Guidetti ^1,

1.	Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna

Received January 2014 Revised August 2014 Published October 2014

Abstract
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We discuss two inverse problems of reconstruction of data in a mixed parabolic integrodifferential problem. First, we shall consider the reconstruction on a factor depending on time in the source term. Next, we shall consider the reconstruction of a convolution kernel.

Keywords: convolution kernels., inverse problems, Integrodifferential parabolic problems, memory operators.

Mathematics Subject Classification: 35K15, 65M32, 47G2.

Citation: Davide Guidetti. Some inverse problems of identification for integrodifferential parabolic systems with a boundary memory term. Discrete and Continuous Dynamical Systems - S, 2015, 8 (4) : 749-756. doi: 10.3934/dcdss.2015.8.749

References:

[1]	C. Cavaterra and F. Colombo, Identifying a heat source in automatic control problems, Comm. Appl. Nonlinear Anal., 11 (2014), 1-23.
[2]	C. Cavaterra and D. Guidetti, Identification of a convolution kernel in a control problem for the heat equation with a boundary memory term, Ann. Mat. Pura Appl., 193 (2014), 779-816. doi: 10.1007/s10231-012-0301-y.
[3]	C. Cavaterra and D. Guidetti, Identification of a source factor in a control problem for the heat equation with a boundary memory term,, submitted., ().
[4]	P. Colli, M. Grasselli and J. Sprekels, Automatic control via thermostats of a hyperbolic Stefan problem with memory, Appl. Math. Optim., 39 (1999), 229-255. doi: 10.1007/s002459900105.
[5]	L. De Simon, Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine, Rend. Sem. Mat. Univ. Padova, 34 (1964), 205-223.
[6]	D. Guidetti, Some remarks on operators preserving oscillations,, to appear in Rend. Sem. Mat.Univ. Pol. Torino., ().
[7]	M. Krasnosel'skii and A. Pokrovskii, Systems with Hysteresis, Springer-Verlag, Berlin, 1989. doi: 10.1007/978-3-642-61302-9.
[8]	O. A. Ladyzhenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs, AMS, 1968.
[9]	J. L. Lions and E. Magenes, Problémes Aux Limites Non Homogénes et Applications, Vol. II, Springer-Verlag, 1972.
[10]	A. I. Prilepko, D. G. Orlovsky and I. A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Monographs and Textbooks in Pure and Applied Mathematics, 231, Marcel Dekker, Inc., New York, 2000.
[11]	H. Triebel, Theory of Function Spaces, Birkhäuser, 1983. doi: 10.1007/978-3-0346-0416-1.
[12]	A. Visintin, Differential Models in Hysteresis, Applied Mathematical Sciences, 111, Springer-Verlag, Berlin, 1994. doi: 10.1007/978-3-662-11557-2.

show all references

References:

[1]	C. Cavaterra and F. Colombo, Identifying a heat source in automatic control problems, Comm. Appl. Nonlinear Anal., 11 (2014), 1-23.
[2]	C. Cavaterra and D. Guidetti, Identification of a convolution kernel in a control problem for the heat equation with a boundary memory term, Ann. Mat. Pura Appl., 193 (2014), 779-816. doi: 10.1007/s10231-012-0301-y.
[3]	C. Cavaterra and D. Guidetti, Identification of a source factor in a control problem for the heat equation with a boundary memory term,, submitted., ().
[4]	P. Colli, M. Grasselli and J. Sprekels, Automatic control via thermostats of a hyperbolic Stefan problem with memory, Appl. Math. Optim., 39 (1999), 229-255. doi: 10.1007/s002459900105.
[5]	L. De Simon, Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine, Rend. Sem. Mat. Univ. Padova, 34 (1964), 205-223.
[6]	D. Guidetti, Some remarks on operators preserving oscillations,, to appear in Rend. Sem. Mat.Univ. Pol. Torino., ().
[7]	M. Krasnosel'skii and A. Pokrovskii, Systems with Hysteresis, Springer-Verlag, Berlin, 1989. doi: 10.1007/978-3-642-61302-9.
[8]	O. A. Ladyzhenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs, AMS, 1968.
[9]	J. L. Lions and E. Magenes, Problémes Aux Limites Non Homogénes et Applications, Vol. II, Springer-Verlag, 1972.
[10]	A. I. Prilepko, D. G. Orlovsky and I. A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Monographs and Textbooks in Pure and Applied Mathematics, 231, Marcel Dekker, Inc., New York, 2000.
[11]	H. Triebel, Theory of Function Spaces, Birkhäuser, 1983. doi: 10.1007/978-3-0346-0416-1.
[12]	A. Visintin, Differential Models in Hysteresis, Applied Mathematical Sciences, 111, Springer-Verlag, Berlin, 1994. doi: 10.1007/978-3-662-11557-2.

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