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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

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 & 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.  Google Scholar

[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.  Google Scholar

[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., ().   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[6]

D. Guidetti, Some remarks on operators preserving oscillations,, to appear in Rend. Sem. Mat.Univ. Pol. Torino., ().   Google Scholar

[7]

M. Krasnosel'skii and A. Pokrovskii, Systems with Hysteresis, Springer-Verlag, Berlin, 1989. doi: 10.1007/978-3-642-61302-9.  Google Scholar

[8]

O. A. Ladyzhenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs, AMS, 1968.  Google Scholar

[9]

J. L. Lions and E. Magenes, Problémes Aux Limites Non Homogénes et Applications, Vol. II, Springer-Verlag, 1972. Google Scholar

[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.  Google Scholar

[11]

H. Triebel, Theory of Function Spaces, Birkhäuser, 1983. doi: 10.1007/978-3-0346-0416-1.  Google Scholar

[12]

A. Visintin, Differential Models in Hysteresis, Applied Mathematical Sciences, 111, Springer-Verlag, Berlin, 1994. doi: 10.1007/978-3-662-11557-2.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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., ().   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[6]

D. Guidetti, Some remarks on operators preserving oscillations,, to appear in Rend. Sem. Mat.Univ. Pol. Torino., ().   Google Scholar

[7]

M. Krasnosel'skii and A. Pokrovskii, Systems with Hysteresis, Springer-Verlag, Berlin, 1989. doi: 10.1007/978-3-642-61302-9.  Google Scholar

[8]

O. A. Ladyzhenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs, AMS, 1968.  Google Scholar

[9]

J. L. Lions and E. Magenes, Problémes Aux Limites Non Homogénes et Applications, Vol. II, Springer-Verlag, 1972. Google Scholar

[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.  Google Scholar

[11]

H. Triebel, Theory of Function Spaces, Birkhäuser, 1983. doi: 10.1007/978-3-0346-0416-1.  Google Scholar

[12]

A. Visintin, Differential Models in Hysteresis, Applied Mathematical Sciences, 111, Springer-Verlag, Berlin, 1994. doi: 10.1007/978-3-662-11557-2.  Google Scholar

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