American Institute of Mathematical Sciences

Advanced
2015, 2015(special): 428-435. doi: 10.3934/proc.2015.0428

A general approach to identification problems and applications to partial differential equations

Angelo Favini 1,

1. 

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

Received  August 2014 Revised  May 2015 Published  November 2015

An abstract method to deal with identification problems related to evolution equations with multivalued linear operators (or linear relations) is described. Some applications to partial differential equations are presented.
Keywords: existence and uniqueness of solutions to inverse problems., linear parabolic diff erential equations, Direct and Inverse Problems, First order equations in Banach spaces.
Mathematics Subject Classification: 35R30, 34610, 35K20, 45N05, 45Q0.
Citation: Angelo Favini. A general approach to identification problems and applications to partial differential equations. Conference Publications, 2015, 2015 (special) : 428-435. doi: 10.3934/proc.2015.0428
References:
[1]

A. Favaron and A. Favini, On the behavior of singular semigroups in intermediatic and interpolation spaces and its applications to maximal regularity for degenerate integrodifferential equations, Abstract and Applied Analysis, Artide ID 279454, 37 pages, 2013.  Google Scholar

[2]

A. Favaron, A. Favini and H. Tanabe, Perturbation Methods for inverse Problems in degenerate differential Equations,, to appear., ().   Google Scholar

[3]

A. Favini, A. Lorenzi, G. Marinoschi and H. Tanabe, Perturbation Methods and Identification Problems for Degenerate Evolution Equations, Mathematics Invited Contributors at the Seventh Congress of Romanian Mathematicians, Brasov 2011 (eds. L. Beznea, V. Brinzanescu, M. Iosifescu, G. Marinoschi, R. Purice, and D. Timotin), Publishing house of the Romanian Academy (2013), 88-96. Google Scholar

[4]

A. Favini, A. Lorenzi and H. Tanabe, A general Approach to Identification Problems, New Prospects in Direct, Inverse and Control Problems for Evolution Equations, (eds. A. Favini, G. Fragnelli, and R. M. Mininni), Springer INdAM Series 10, Springer, Cham, Heidelberg, New York, Dordrecht, London, (2014), 107-119. Google Scholar

[5]

A. Favini, A. Lorenzi and H. Tanabe, Degenerate Integrodifferential Equations of Parabolyc Type with Robin boundary conditions: $L^p$-theory,, preprint., ().   Google Scholar

[6]

A. Favini, A. Lorenzi and H. Tanabe, Direct and Inverse Degenerate Parabolic Differential Equations with Multivalued Operators, Electronic J. Diff. Eqs, (2015), 1-22. Google Scholar

[7]

A. Favini, A. Lorenzi and H. Tanabe, Direct and Inverse Problems for Systems of Singular Differential Boundary Value Problems, Electronic J. Diff. Eqs, (2012), 1-34.  Google Scholar

[8]

A. Favini and G. Marinoschi, Identification for degenerate problems of hyperbolic type, Applicable Analysis 91(78), (2012), 1451-1468. Google Scholar

[9]

A. Favini and H. Tanabe, Degenerate Differential Equations of Parabolic Type and Inverse Problems, Proceedings of Seminar on Partial Differential Equations in Osaka, Osaka University, August 20-24, 2012, (2013), 89-100. Google Scholar

[10]

A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Monographs and Textbooks in Pure and Applied Mathematics 215, M. Dekker Inc, New York, (1999).  Google Scholar

[11]

S. G. Kreĭn, Differential Equations in Banach Spaces, Translations of Mathematical Monography AMS, (1972).  Google Scholar

[12]

A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser Basol (1995).  Google Scholar

show all references

References:
[1]

A. Favaron and A. Favini, On the behavior of singular semigroups in intermediatic and interpolation spaces and its applications to maximal regularity for degenerate integrodifferential equations, Abstract and Applied Analysis, Artide ID 279454, 37 pages, 2013.  Google Scholar

[2]

A. Favaron, A. Favini and H. Tanabe, Perturbation Methods for inverse Problems in degenerate differential Equations,, to appear., ().   Google Scholar

[3]

A. Favini, A. Lorenzi, G. Marinoschi and H. Tanabe, Perturbation Methods and Identification Problems for Degenerate Evolution Equations, Mathematics Invited Contributors at the Seventh Congress of Romanian Mathematicians, Brasov 2011 (eds. L. Beznea, V. Brinzanescu, M. Iosifescu, G. Marinoschi, R. Purice, and D. Timotin), Publishing house of the Romanian Academy (2013), 88-96. Google Scholar

[4]

A. Favini, A. Lorenzi and H. Tanabe, A general Approach to Identification Problems, New Prospects in Direct, Inverse and Control Problems for Evolution Equations, (eds. A. Favini, G. Fragnelli, and R. M. Mininni), Springer INdAM Series 10, Springer, Cham, Heidelberg, New York, Dordrecht, London, (2014), 107-119. Google Scholar

[5]

A. Favini, A. Lorenzi and H. Tanabe, Degenerate Integrodifferential Equations of Parabolyc Type with Robin boundary conditions: $L^p$-theory,, preprint., ().   Google Scholar

[6]

A. Favini, A. Lorenzi and H. Tanabe, Direct and Inverse Degenerate Parabolic Differential Equations with Multivalued Operators, Electronic J. Diff. Eqs, (2015), 1-22. Google Scholar

[7]

A. Favini, A. Lorenzi and H. Tanabe, Direct and Inverse Problems for Systems of Singular Differential Boundary Value Problems, Electronic J. Diff. Eqs, (2012), 1-34.  Google Scholar

[8]

A. Favini and G. Marinoschi, Identification for degenerate problems of hyperbolic type, Applicable Analysis 91(78), (2012), 1451-1468. Google Scholar

[9]

A. Favini and H. Tanabe, Degenerate Differential Equations of Parabolic Type and Inverse Problems, Proceedings of Seminar on Partial Differential Equations in Osaka, Osaka University, August 20-24, 2012, (2013), 89-100. Google Scholar

[10]

A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Monographs and Textbooks in Pure and Applied Mathematics 215, M. Dekker Inc, New York, (1999).  Google Scholar

[11]

S. G. Kreĭn, Differential Equations in Banach Spaces, Translations of Mathematical Monography AMS, (1972).  Google Scholar

[12]

A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser Basol (1995).  Google Scholar

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