Inverse problems for singular differential-operator equations with higher order polar singularities

Previous Article
Strain gradient theory of porous solids with initial stresses and initial heat flux
DCDS-B Home
This Issue
Next Article
Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids

September 2014, 19(7): 2159-2168. doi: 10.3934/dcdsb.2014.19.2159

Inverse problems for singular differential-operator equations with higher order polar singularities

Mohammed Al Horani ^1, and Angelo Favini ^2,

1.	Department of Mathematics, The University of Jordan, Amman, Jordan
2.	Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna

Received May 2013 Revised April 2014 Published August 2014

Abstract
Related Papers

In this paper we study an inverse problem for strongly degenerate differential equations in Banach spaces. Projection method on suitable subspaces will be used to solve the given problem. A number of concrete applications to ordinary and partial differential equations is described.

Keywords: Banach space., Identification problem, first order equations, degenerate equation, inverse problem.

Mathematics Subject Classification: Primary: 34G10; Secondary: 34A5.

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

References:

[1]	M. Al Horani and A. Favini, Perturbation method for first and complete second order differential equations, Preprint.
[2]	M. Al Horani and A. Favini, An identification problem for first-order degenerate differential equations, Journal of Optimization Theory and Applications, 130 (2006), 41-60. doi: 10.1007/s10957-006-9083-y.
[3]	R. Cross, A. Favini and Y. Yakubov, Perturbation results for multivalued linear operators, Progress in Nonlinear Differential Equations and Their Applications, 80 (2011), 111-130. doi: 10.1007/978-3-0348-0075-4_7.
[4]	G. V. Demidenko and S. V. Uspenskii, Partial Differential Equations and Systems not Solvable With Respect to the Highest-Order Derivative, Marcel Dekker, Inc., New York, 2003. doi: 10.1201/9780203911433.
[5]	A. Favaron and A. Favini, Fractional powers and interpolation theory for multivalued linear operators and applications to degenerate differential equations, Tsukuba J. Math., 35 (2011), 259-323.
[6]	A. Faviniand and G. Marinoschi, Identification for degenerate problems of hyperbolic type, Applicable Analysis, 91 (2012), 1511-1527. doi: 10.1080/00036811.2011.630665.
[7]	A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc. New York, 1999.
[8]	F. Kappel and H. W. Knobloch, Gewöhnliche Differentialgleichungen, B. G. Teubner, Stuttgart, 1974.
[9]	A. E. Taylor, Introduction to Functional Analysis, John Wiley & Sons, New York, 1958.
[10]	H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amesterdam, 1978.
[11]	L. A. Vlasenko, Evolutionary Models with Implicit and Degenerate Differential Equations, (rus.)- Dnepropetrovsk: System Technology, 2006.
[12]	K. Yosida, Functional Analysis, $6^{th}$ ed, Springer Verlag, Berlin-Heidelberg, New York, 1980.
[13]	S. Yakubov and Y. Yakubov, Differential-operator Equations. Ordinary and Partial Differential Equations, Chapman & Hall, Boca Raton, USA, 2000.

show all references

References:

[1]	M. Al Horani and A. Favini, Perturbation method for first and complete second order differential equations, Preprint.
[2]	M. Al Horani and A. Favini, An identification problem for first-order degenerate differential equations, Journal of Optimization Theory and Applications, 130 (2006), 41-60. doi: 10.1007/s10957-006-9083-y.
[3]	R. Cross, A. Favini and Y. Yakubov, Perturbation results for multivalued linear operators, Progress in Nonlinear Differential Equations and Their Applications, 80 (2011), 111-130. doi: 10.1007/978-3-0348-0075-4_7.
[4]	G. V. Demidenko and S. V. Uspenskii, Partial Differential Equations and Systems not Solvable With Respect to the Highest-Order Derivative, Marcel Dekker, Inc., New York, 2003. doi: 10.1201/9780203911433.
[5]	A. Favaron and A. Favini, Fractional powers and interpolation theory for multivalued linear operators and applications to degenerate differential equations, Tsukuba J. Math., 35 (2011), 259-323.
[6]	A. Faviniand and G. Marinoschi, Identification for degenerate problems of hyperbolic type, Applicable Analysis, 91 (2012), 1511-1527. doi: 10.1080/00036811.2011.630665.
[7]	A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc. New York, 1999.
[8]	F. Kappel and H. W. Knobloch, Gewöhnliche Differentialgleichungen, B. G. Teubner, Stuttgart, 1974.
[9]	A. E. Taylor, Introduction to Functional Analysis, John Wiley & Sons, New York, 1958.
[10]	H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amesterdam, 1978.
[11]	L. A. Vlasenko, Evolutionary Models with Implicit and Degenerate Differential Equations, (rus.)- Dnepropetrovsk: System Technology, 2006.
[12]	K. Yosida, Functional Analysis, $6^{th}$ ed, Springer Verlag, Berlin-Heidelberg, New York, 1980.
[13]	S. Yakubov and Y. Yakubov, Differential-operator Equations. Ordinary and Partial Differential Equations, Chapman & Hall, Boca Raton, USA, 2000.

[1]	Viorel Barbu, Gabriela Marinoschi. An identification problem for a linear evolution equation in a banach space. Discrete and Continuous Dynamical Systems - S, 2020, 13 (5) : 1429-1440. doi: 10.3934/dcdss.2020081
[2]	Alfredo Lorenzi, Ioan I. Vrabie. An identification problem for a linear evolution equation in a Banach space and applications. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 671-691. doi: 10.3934/dcdss.2011.4.671
[3]	Atsushi Kawamoto. Hölder stability estimate in an inverse source problem for a first and half order time fractional diffusion equation. Inverse Problems and Imaging, 2018, 12 (2) : 315-330. doi: 10.3934/ipi.2018014
[4]	Vladimir E. Fedorov, Natalia D. Ivanova. Identification problem for a degenerate evolution equation with overdetermination on the solution semigroup kernel. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 687-696. doi: 10.3934/dcdss.2016022
[5]	Rehana Naz, Fazal M Mahomed, Azam Chaudhry. First integrals of Hamiltonian systems: The inverse problem. Discrete and Continuous Dynamical Systems - S, 2020, 13 (10) : 2829-2840. doi: 10.3934/dcdss.2020121
[6]	Mohammed Al Horani, Angelo Favini. First-order inverse evolution equations. Evolution Equations and Control Theory, 2014, 3 (3) : 355-361. doi: 10.3934/eect.2014.3.355
[7]	M. Nakamura, Tohru Ozawa. The Cauchy problem for nonlinear wave equations in the Sobolev space of critical order. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 215-231. doi: 10.3934/dcds.1999.5.215
[8]	J. Carmelo Flores, Luz De Teresa. Null controllability of one dimensional degenerate parabolic equations with first order terms. Discrete and Continuous Dynamical Systems - B, 2020, 25 (10) : 3963-3981. doi: 10.3934/dcdsb.2020136
[9]	Nguyen Huy Tuan, Mokhtar Kirane, Long Dinh Le, Van Thinh Nguyen. On an inverse problem for fractional evolution equation. Evolution Equations and Control Theory, 2017, 6 (1) : 111-134. doi: 10.3934/eect.2017007
[10]	Fabio Camilli, Francisco Silva. A semi-discrete approximation for a first order mean field game problem. Networks and Heterogeneous Media, 2012, 7 (2) : 263-277. doi: 10.3934/nhm.2012.7.263
[11]	Monika Laskawy. Optimality conditions of the first eigenvalue of a fourth order Steklov problem. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1843-1859. doi: 10.3934/cpaa.2017089
[12]	Alfredo Lorenzi, Eugenio Sinestrari. An identification problem for a nonlinear one-dimensional wave equation. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5253-5271. doi: 10.3934/dcds.2013.33.5253
[13]	Luciano Pandolfi. Riesz systems, spectral controllability and a source identification problem for heat equations with memory. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 745-759. doi: 10.3934/dcdss.2011.4.745
[14]	Valter Pohjola. An inverse problem for the magnetic Schrödinger operator on a half space with partial data. Inverse Problems and Imaging, 2014, 8 (4) : 1169-1189. doi: 10.3934/ipi.2014.8.1169
[15]	Gen Nakamura, Michiyuki Watanabe. An inverse boundary value problem for a nonlinear wave equation. Inverse Problems and Imaging, 2008, 2 (1) : 121-131. doi: 10.3934/ipi.2008.2.121
[16]	Xiaoli Feng, Meixia Zhao, Peijun Li, Xu Wang. An inverse source problem for the stochastic wave equation. Inverse Problems and Imaging, 2022, 16 (2) : 397-415. doi: 10.3934/ipi.2021055
[17]	Gisella Croce. An elliptic problem with degenerate coercivity and a singular quadratic gradient lower order term. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 507-530. doi: 10.3934/dcdss.2012.5.507
[18]	Ciro D'Apice, Olha P. Kupenko, Rosanna Manzo. On boundary optimal control problem for an arterial system: First-order optimality conditions. Networks and Heterogeneous Media, 2018, 13 (4) : 585-607. doi: 10.3934/nhm.2018027
[19]	Diogo A. Gomes, Hiroyoshi Mitake, Kengo Terai. The selection problem for some first-order stationary Mean-field games. Networks and Heterogeneous Media, 2020, 15 (4) : 681-710. doi: 10.3934/nhm.2020019
[20]	Yanbo Hu, Tong Li. The regularity of a degenerate Goursat problem for the 2-D isothermal Euler equations. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3317-3336. doi: 10.3934/cpaa.2019149

2021 Impact Factor: 1.497

Tools

Metrics

Other articles
by authors

on AIMS
Mohammed Al Horani Angelo Favini
on Google Scholar
Mohammed Al Horani Angelo Favini

[Back to Top]