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

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

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.
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, (2794).   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, (2013), 88.   Google Scholar

[4]

A. Favini, A. Lorenzi and H. Tanabe, A general Approach to Identification Problems,, New Prospects in Direct, (2014), 107.   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.   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.   Google Scholar

[8]

A. Favini and G. Marinoschi, Identification for degenerate problems of hyperbolic type,, Applicable Analysis 91(78), 91 (2012), 1451.   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, (2013), 20.   Google Scholar

[10]

A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces,, Monographs and Textbooks in Pure and Applied Mathematics 215, (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)., (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, (2794).   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, (2013), 88.   Google Scholar

[4]

A. Favini, A. Lorenzi and H. Tanabe, A general Approach to Identification Problems,, New Prospects in Direct, (2014), 107.   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.   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.   Google Scholar

[8]

A. Favini and G. Marinoschi, Identification for degenerate problems of hyperbolic type,, Applicable Analysis 91(78), 91 (2012), 1451.   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, (2013), 20.   Google Scholar

[10]

A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces,, Monographs and Textbooks in Pure and Applied Mathematics 215, (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)., (1995).   Google Scholar

[1]

Mohammed Al Horani, Angelo Favini. First-order inverse evolution equations. Evolution Equations & Control Theory, 2014, 3 (3) : 355-361. doi: 10.3934/eect.2014.3.355

[2]

Angelo Favini, Yakov Yakubov. Regular boundary value problems for ordinary differential-operator equations of higher order in UMD Banach spaces. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 595-614. doi: 10.3934/dcdss.2011.4.595

[3]

Tan Bui-Thanh, Omar Ghattas. Analysis of the Hessian for inverse scattering problems. Part III: Inverse medium scattering of electromagnetic waves in three dimensions. Inverse Problems & Imaging, 2013, 7 (4) : 1139-1155. doi: 10.3934/ipi.2013.7.1139

[4]

Shiyun Wang, Yong-Jin Liu, Yong Jiang. A majorized penalty approach to inverse linear second order cone programming problems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 965-976. doi: 10.3934/jimo.2014.10.965

[5]

Y. Gong, X. Xiang. A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales. Journal of Industrial & Management Optimization, 2009, 5 (1) : 1-10. doi: 10.3934/jimo.2009.5.1

[6]

Davide Guidetti. Convergence to a stationary state of solutions to inverse problems of parabolic type. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 711-722. doi: 10.3934/dcdss.2013.6.711

[7]

Jaan Janno, Kairi Kasemets. A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination. Inverse Problems & Imaging, 2009, 3 (1) : 17-41. doi: 10.3934/ipi.2009.3.17

[8]

Sergiy Zhuk. Inverse problems for linear ill-posed differential-algebraic equations with uncertain parameters. Conference Publications, 2011, 2011 (Special) : 1467-1476. doi: 10.3934/proc.2011.2011.1467

[9]

Johannes Elschner, Guanghui Hu. Uniqueness in inverse transmission scattering problems for multilayered obstacles. Inverse Problems & Imaging, 2011, 5 (4) : 793-813. doi: 10.3934/ipi.2011.5.793

[10]

Mohammed Al Horani, Angelo Favini. Inverse problems for singular differential-operator equations with higher order polar singularities. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2159-2168. doi: 10.3934/dcdsb.2014.19.2159

[11]

Gabriella Di Blasio, Alfredo Lorenzi. Direct and inverse problems in age--structured population diffusion. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 539-563. doi: 10.3934/dcdss.2011.4.539

[12]

Sari Lasanen. Non-Gaussian statistical inverse problems. Part II: Posterior convergence for approximated unknowns. Inverse Problems & Imaging, 2012, 6 (2) : 267-287. doi: 10.3934/ipi.2012.6.267

[13]

Sari Lasanen. Non-Gaussian statistical inverse problems. Part I: Posterior distributions. Inverse Problems & Imaging, 2012, 6 (2) : 215-266. doi: 10.3934/ipi.2012.6.215

[14]

Fatihcan M. Atay, Lavinia Roncoroni. Lumpability of linear evolution Equations in Banach spaces. Evolution Equations & Control Theory, 2017, 6 (1) : 15-34. doi: 10.3934/eect.2017002

[15]

Anna Doubova, Enrique Fernández-Cara. Some geometric inverse problems for the linear wave equation. Inverse Problems & Imaging, 2015, 9 (2) : 371-393. doi: 10.3934/ipi.2015.9.371

[16]

Daijun Jiang, Hui Feng, Jun Zou. Overlapping domain decomposition methods for linear inverse problems. Inverse Problems & Imaging, 2015, 9 (1) : 163-188. doi: 10.3934/ipi.2015.9.163

[17]

Mehdi Badra, Fabien Caubet, Jérémi Dardé. Stability estimates for Navier-Stokes equations and application to inverse problems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2379-2407. doi: 10.3934/dcdsb.2016052

[18]

Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Inverse problems for evolution equations with time dependent operator-coefficients. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 737-744. doi: 10.3934/dcdss.2016025

[19]

Fioralba Cakoni, Rainer Kress. Integral equations for inverse problems in corrosion detection from partial Cauchy data. Inverse Problems & Imaging, 2007, 1 (2) : 229-245. doi: 10.3934/ipi.2007.1.229

[20]

Peter Poláčik. On uniqueness of positive entire solutions and other properties of linear parabolic equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 13-26. doi: 10.3934/dcds.2005.12.13

 Impact Factor: 

Metrics

  • PDF downloads (18)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]