August  2009, 3(3): 505-536. doi: 10.3934/ipi.2009.3.505

Regularity and identification for an integrodifferential one-dimensional hyperbolic equation

1. 

Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano

2. 

Dipartimento di Matematica, Università di Roma “La Sapienza”, P.le A. Moro 5, 00185 Roma

Received  October 2008 Revised  May 2009 Published  July 2009

In this paper we determine a (possibly) non-continuous scalar relaxation kernel of bounded variation in an integrodifferential equation related to a Banach space when a nonlocal additional measurement involving the state function is available. We prove a result concerning global existence and uniqueness.
   An application is given, in the framework of space of continuous functions, to the case of one-dimensional hyperbolic second-order integrodifferential equations endowed with initial and Dirichlet boundary conditions.
Citation: Alfredo Lorenzi, Eugenio Sinestrari. Regularity and identification for an integrodifferential one-dimensional hyperbolic equation. Inverse Problems and Imaging, 2009, 3 (3) : 505-536. doi: 10.3934/ipi.2009.3.505
[1]

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

[2]

Priscila Santos Ramos, J. Vanterler da C. Sousa, E. Capelas de Oliveira. Existence and uniqueness of mild solutions for quasi-linear fractional integro-differential equations. Evolution Equations and Control Theory, 2022, 11 (1) : 1-24. doi: 10.3934/eect.2020100

[3]

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

[4]

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

[5]

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

[6]

Kun-Peng Jin, Jin Liang, Ti-Jun Xiao. Uniform polynomial stability of second order integro-differential equations in Hilbert spaces with positive definite kernels. Discrete and Continuous Dynamical Systems - S, 2021, 14 (9) : 3141-3166. doi: 10.3934/dcdss.2021077

[7]

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

[8]

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

[9]

Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Inverse problems on degenerate integro-differential equations. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022025

[10]

Seda İğret Araz. New class of volterra integro-differential equations with fractal-fractional operators: Existence, uniqueness and numerical scheme. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2297-2309. doi: 10.3934/dcdss.2021053

[11]

Cyril Imbert, Sylvia Serfaty. Repeated games for non-linear parabolic integro-differential equations and integral curvature flows. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1517-1552. doi: 10.3934/dcds.2011.29.1517

[12]

Faranak Rabiei, Fatin Abd Hamid, Zanariah Abd Majid, Fudziah Ismail. Numerical solutions of Volterra integro-differential equations using General Linear Method. Numerical Algebra, Control and Optimization, 2019, 9 (4) : 433-444. doi: 10.3934/naco.2019042

[13]

Ankit Kumar, Kamal Jeet, Ramesh Kumar Vats. Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space. Evolution Equations and Control Theory, 2022, 11 (2) : 605-619. doi: 10.3934/eect.2021016

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[19]

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

[20]

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

2021 Impact Factor: 1.483

Metrics

  • PDF downloads (67)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]