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

1. 

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

Received  January 2014 Revised  August 2014 Published  October 2014

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.
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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