doi: 10.3934/eect.2021051
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Singular integro-differential equations with applications

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, Italy

3. 

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

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

Received  January 2021 Revised  August 2021 Early access September 2021

We are devoted with singular integro-differential abstract Cauchyproblems. Required conditions on spaces and operators are givenguaranteeing existence and uniqueness of solutions. Applications from partial differential equations are given to illustrate the abstract singular integro-differential problem.

Citation: Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Singular integro-differential equations with applications. Evolution Equations & Control Theory, doi: 10.3934/eect.2021051
References:
[1]

M. Al HoraniM. FabrizioA. Favini and H. Tanabe, Direct and inverse problems for degenerate differential equations, Ann. Univ. Ferrara, 64 (2018), 227-241.  doi: 10.1007/s11565-018-0303-9.  Google Scholar

[2]

M. Al Horani, M. Fabrizio, A. Favini and H. Tanabe, Identification problems for degenerate integro-differential equations, In Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs, (eds. P. Colli, A. Favini, E. Rocca, G. Schimperna and J. Sprekels), Springer INDAM Series, 22 (2017), 55–75.  Google Scholar

[3]

K. Balachandran and S. Kiruthika, Existence of solutions of abstract fractional integrodifferential equations of Sobolev type, Comput. Math. Appl., 64 (2012), 3406-3413.  doi: 10.1016/j.camwa.2011.12.051.  Google Scholar

[4]

T. Binz and K. J. Engel, Operators with Wentzell boundary conditions and the Dirichlet-to-Neumann operator, Math. Nachr., 292 (2018), 733-746.  doi: 10.1002/mana.201800064.  Google Scholar

[5]

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), 1-37.  doi: 10.1155/2013/275494.  Google Scholar

[6]

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.  doi: 10.21099/tkbjm/1331658708.  Google Scholar

[7]

A. Favaron, Perturbation methods for inverse problems on degenerate differential equations, preprint, (2012), 83–103  Google Scholar

[8]

A. FaviniA. Lorenzi and H. Tanabe, Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: $L^{p}-$theory, J. Math. Anal. Appl., 447 (2017), 579-665.  doi: 10.1016/j.jmaa.2016.10.029.  Google Scholar

[9]

A. Favini, A. Lorenzi and H. Tanabe, Direct and inverse degenerate parabolic differential equations with multi-valued operators, Electronic J. Differential Equations, (2015), 22pp.  Google Scholar

[10]

A. FaviniA. Lorenzi and H. Tanabe, Singular evolution integro-differential equations with kernels defined on bounded intervals, Appl. Anal., 84 (2005), 463-497.  doi: 10.1080/00036810410001724418.  Google Scholar

[11]

A. FaviniA. Lorenzi and H. Tanabe, Singular integro-differential equations of parabolic type, Adv. Differential Equations, 7 (2002), 769-798.   Google Scholar

[12]

A. Favini and H. Tanabe, Degenerate differential equations of parabolic type and inverse problems, Proceeding, Seminar on Partial Differential Equations, Osaka University, Osaka, (2015), 89–100. Google Scholar

[13]

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

[14]

O. A. Oleinik and E. V. Radkevich, The method of introducing a parameter in the study of evolutionary equations, Russian Mathematical Surveys, 33 (1978), 7-84.   Google Scholar

[15]

O. A. Oleinik and E. V. Radkevich, Second order equations with nonnegative characteristic form, Mat. Anal., (1969), 7–252.  Google Scholar

show all references

References:
[1]

M. Al HoraniM. FabrizioA. Favini and H. Tanabe, Direct and inverse problems for degenerate differential equations, Ann. Univ. Ferrara, 64 (2018), 227-241.  doi: 10.1007/s11565-018-0303-9.  Google Scholar

[2]

M. Al Horani, M. Fabrizio, A. Favini and H. Tanabe, Identification problems for degenerate integro-differential equations, In Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs, (eds. P. Colli, A. Favini, E. Rocca, G. Schimperna and J. Sprekels), Springer INDAM Series, 22 (2017), 55–75.  Google Scholar

[3]

K. Balachandran and S. Kiruthika, Existence of solutions of abstract fractional integrodifferential equations of Sobolev type, Comput. Math. Appl., 64 (2012), 3406-3413.  doi: 10.1016/j.camwa.2011.12.051.  Google Scholar

[4]

T. Binz and K. J. Engel, Operators with Wentzell boundary conditions and the Dirichlet-to-Neumann operator, Math. Nachr., 292 (2018), 733-746.  doi: 10.1002/mana.201800064.  Google Scholar

[5]

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), 1-37.  doi: 10.1155/2013/275494.  Google Scholar

[6]

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.  doi: 10.21099/tkbjm/1331658708.  Google Scholar

[7]

A. Favaron, Perturbation methods for inverse problems on degenerate differential equations, preprint, (2012), 83–103  Google Scholar

[8]

A. FaviniA. Lorenzi and H. Tanabe, Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: $L^{p}-$theory, J. Math. Anal. Appl., 447 (2017), 579-665.  doi: 10.1016/j.jmaa.2016.10.029.  Google Scholar

[9]

A. Favini, A. Lorenzi and H. Tanabe, Direct and inverse degenerate parabolic differential equations with multi-valued operators, Electronic J. Differential Equations, (2015), 22pp.  Google Scholar

[10]

A. FaviniA. Lorenzi and H. Tanabe, Singular evolution integro-differential equations with kernels defined on bounded intervals, Appl. Anal., 84 (2005), 463-497.  doi: 10.1080/00036810410001724418.  Google Scholar

[11]

A. FaviniA. Lorenzi and H. Tanabe, Singular integro-differential equations of parabolic type, Adv. Differential Equations, 7 (2002), 769-798.   Google Scholar

[12]

A. Favini and H. Tanabe, Degenerate differential equations of parabolic type and inverse problems, Proceeding, Seminar on Partial Differential Equations, Osaka University, Osaka, (2015), 89–100. Google Scholar

[13]

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

[14]

O. A. Oleinik and E. V. Radkevich, The method of introducing a parameter in the study of evolutionary equations, Russian Mathematical Surveys, 33 (1978), 7-84.   Google Scholar

[15]

O. A. Oleinik and E. V. Radkevich, Second order equations with nonnegative characteristic form, Mat. Anal., (1969), 7–252.  Google Scholar

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