• Previous Article
    On solution manifolds of differential systems with discrete state-dependent delays
  • DCDS-S Home
  • This Issue
  • Next Article
    Comparison of simulation-based algorithms for parameter estimation and state reconstruction in nonlinear state-space models
doi: 10.3934/dcdss.2022025
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Inverse problems on degenerate integro-differential equations

1. 

Department of Mathematics, The University of Jordan, Amman, 11942, Jordan

2. 

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

3. 

Takarazuka, Hirai Sanso 12-13,665-0817, Japan

* Corresponding author: Mohammed Al Horani, horani@ju.edu.jo

Received  August 2021 Revised  December 2021 Early access February 2022

We study inverse problems on degenerate integro-differential equations without using maximal regularity property. This seems new at all in the related literature. Some applications to concrete partial differential equations are given.

Citation: Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Inverse problems on degenerate integro-differential equations. Discrete and Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2022025
References:
[1]

M. Al Horani and A. Favini, Degenerate first-order identification problems in Banach spaces, Differential Equations, Inverse and Direct Problems, Taylor and Francis Group, Boca Raton (eds. A. Favini and A. Lorenzi), 1–15, Lect. Notes Pure Appl. Math., 251, Chapman & Hall/CRC, Boca Raton, FL, 2006.

[2]

M. Al Horani and A. Favini, An identification problem for first-order degenerate differential equations, J. Optim. Theory Appl., 130 (2006), 41-60.  doi: 10.1007/s10957-006-9083-y.

[3]

A. Favaron and A. Favini, On the behaviour of singular semigroups in intermediate and interpolation spaces and its applications to maximal regularity for degenerate integro-differential evolution equations, Abstr. Appl. Anal., 2013 (2013), Art. ID 275494, 37 pp. doi: 10.1155/2013/275494.

[4]

A. Favini and H. Tanabe, Perturbation methods for inverse problems on degenerate differential equations, J. Math. Soc. Japan, submitted.

[5]

A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc., New York, 1999.

[6]

P. Grisvard, Spazi di tracce e applicazioni, Rend. Mat., 5 (1972), 657-729. 

[7]

P. Grisvard, Commutativité de Deux Foncteurs d'interpolation et applications, J. Math. Pures Appl., 45 (1966), 207-290. 

[8]

J.-L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math., 19 (1964), 5-68. 

show all references

References:
[1]

M. Al Horani and A. Favini, Degenerate first-order identification problems in Banach spaces, Differential Equations, Inverse and Direct Problems, Taylor and Francis Group, Boca Raton (eds. A. Favini and A. Lorenzi), 1–15, Lect. Notes Pure Appl. Math., 251, Chapman & Hall/CRC, Boca Raton, FL, 2006.

[2]

M. Al Horani and A. Favini, An identification problem for first-order degenerate differential equations, J. Optim. Theory Appl., 130 (2006), 41-60.  doi: 10.1007/s10957-006-9083-y.

[3]

A. Favaron and A. Favini, On the behaviour of singular semigroups in intermediate and interpolation spaces and its applications to maximal regularity for degenerate integro-differential evolution equations, Abstr. Appl. Anal., 2013 (2013), Art. ID 275494, 37 pp. doi: 10.1155/2013/275494.

[4]

A. Favini and H. Tanabe, Perturbation methods for inverse problems on degenerate differential equations, J. Math. Soc. Japan, submitted.

[5]

A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc., New York, 1999.

[6]

P. Grisvard, Spazi di tracce e applicazioni, Rend. Mat., 5 (1972), 657-729. 

[7]

P. Grisvard, Commutativité de Deux Foncteurs d'interpolation et applications, J. Math. Pures Appl., 45 (1966), 207-290. 

[8]

J.-L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math., 19 (1964), 5-68. 

[1]

Tomás Caraballo, P.E. Kloeden. Non-autonomous attractors for integro-differential evolution equations. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 17-36. doi: 10.3934/dcdss.2009.2.17

[2]

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

[3]

Olivier Bonnefon, Jérôme Coville, Jimmy Garnier, Lionel Roques. Inside dynamics of solutions of integro-differential equations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : 3057-3085. doi: 10.3934/dcdsb.2014.19.3057

[4]

Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Singular integro-differential equations with applications. Evolution Equations and Control Theory, 2021  doi: 10.3934/eect.2021051

[5]

Huy Tuan Nguyen, Huu Can Nguyen, Renhai Wang, Yong Zhou. Initial value problem for fractional Volterra integro-differential equations with Caputo derivative. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6483-6510. doi: 10.3934/dcdsb.2021030

[6]

Walter Allegretto, John R. Cannon, Yanping Lin. A parabolic integro-differential equation arising from thermoelastic contact. Discrete and Continuous Dynamical Systems, 1997, 3 (2) : 217-234. doi: 10.3934/dcds.1997.3.217

[7]

Narcisa Apreutesei, Nikolai Bessonov, Vitaly Volpert, Vitali Vougalter. Spatial structures and generalized travelling waves for an integro-differential equation. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 537-557. doi: 10.3934/dcdsb.2010.13.537

[8]

Shihchung Chiang. Numerical optimal unbounded control with a singular integro-differential equation as a constraint. Conference Publications, 2013, 2013 (special) : 129-137. doi: 10.3934/proc.2013.2013.129

[9]

Frederic Abergel, Remi Tachet. A nonlinear partial integro-differential equation from mathematical finance. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 907-917. doi: 10.3934/dcds.2010.27.907

[10]

Samir K. Bhowmik, Dugald B. Duncan, Michael Grinfeld, Gabriel J. Lord. Finite to infinite steady state solutions, bifurcations of an integro-differential equation. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 57-71. doi: 10.3934/dcdsb.2011.16.57

[11]

Yi Cao, Jianhua Wu, Lihe Wang. Fundamental solutions of a class of homogeneous integro-differential elliptic equations. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1237-1256. doi: 10.3934/dcds.2019053

[12]

Yubo Chen, Wan Zhuang. The extreme solutions of PBVP for integro-differential equations with caratheodory functions. Conference Publications, 1998, 1998 (Special) : 160-166. doi: 10.3934/proc.1998.1998.160

[13]

Ramasamy Subashini, Chokkalingam Ravichandran, Kasthurisamy Jothimani, Haci Mehmet Baskonus. Existence results of Hilfer integro-differential equations with fractional order. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 911-923. doi: 10.3934/dcdss.2020053

[14]

Tonny Paul, A. Anguraj. Existence and uniqueness of nonlinear impulsive integro-differential equations. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1191-1198. doi: 10.3934/dcdsb.2006.6.1191

[15]

Narcisa Apreutesei, Arnaud Ducrot, Vitaly Volpert. Travelling waves for integro-differential equations in population dynamics. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 541-561. doi: 10.3934/dcdsb.2009.11.541

[16]

Tianling Jin, Jingang Xiong. Schauder estimates for solutions of linear parabolic integro-differential equations. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5977-5998. doi: 10.3934/dcds.2015.35.5977

[17]

Sertan Alkan. A new solution method for nonlinear fractional integro-differential equations. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1065-1077. doi: 10.3934/dcdss.2015.8.1065

[18]

Eitan Tadmor, Prashant Athavale. Multiscale image representation using novel integro-differential equations. Inverse Problems and Imaging, 2009, 3 (4) : 693-710. doi: 10.3934/ipi.2009.3.693

[19]

Patricio Felmer, Ying Wang. Qualitative properties of positive solutions for mixed integro-differential equations. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 369-393. doi: 10.3934/dcds.2019015

[20]

Sebti Kerbal, Yang Jiang. General integro-differential equations and optimal controls on Banach spaces. Journal of Industrial and Management Optimization, 2007, 3 (1) : 119-128. doi: 10.3934/jimo.2007.3.119

2021 Impact Factor: 1.865

Metrics

  • PDF downloads (209)
  • HTML views (143)
  • Cited by (0)

[Back to Top]