Direct and inverse problems for degenerate differential equations

We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on t...

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Veröffentlicht in:Annali dell'Università di Ferrara. Sezione 7. Scienze matematiche Jg. 64; H. 2; S. 227 - 241
Hauptverfasser: Al Horani, Mohammed, Fabrizio, Mauro, Favini, Angelo, Tanabe, Hiroki
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Milan Springer Milan 01.11.2018
Springer Nature B.V
Schlagworte:
Algebraic Geometry
Analysis
Banach spaces
Geometry
History of Mathematical Sciences
Inverse problems
Mathematical analysis
Mathematics
Mathematics and Statistics
Nondestructive testing
Numerical Analysis
Partial differential equations
34G10
First-order problem
34A55
semigroup
Second-order problem
Periodic solution
Inverse problem
ISSN:0430-3202, 1827-1510
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Abstract We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on ( - ∞ , ∞ ) . Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too.
AbstractList We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on ( - ∞ , ∞ ) . Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too.
We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We indicate sufficient conditions for existence and uniqueness of a solution. Periodic conditions are assumed to improve previous approaches on the abstract problem to work on (-∞,∞). Related inverse problems are discussed, too. All general results are applied to some systems of partial differential equations. Inverse problems for degenerate evolution integro-differential equations might be described, too.
Author Tanabe, Hiroki
Favini, Angelo
Fabrizio, Mauro
Al Horani, Mohammed
Author_xml – sequence: 1
  givenname: Mohammed
  orcidid: 0000-0003-4853-6616
  surname: Al Horani
  fullname: Al Horani, Mohammed
  organization: Department of Mathematics, The University of Jordan
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  givenname: Mauro
  orcidid: 0000-0003-0920-2963
  surname: Fabrizio
  fullname: Fabrizio, Mauro
  email: mauro.fabrizio@unibo.it
  organization: Dipartimento di Matematica, Universita di Bologna
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  givenname: Angelo
  surname: Favini
  fullname: Favini, Angelo
  organization: Dipartimento di Matematica, Universita di Bologna
– sequence: 4
  givenname: Hiroki
  surname: Tanabe
  fullname: Tanabe, Hiroki
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10.1016/0022-247X(89)90060-7
10.3934/dcdss.2016025
10.1142/9789813142862_0013
10.1007/978-3-0348-0087-7
10.1007/s00032-016-0260-7
10.1007/BF01759029
10.1155/S1085337501000537
10.1007/s10957-015-0733-9
10.1016/0022-0396(91)90153-Z
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Keywords 34G10
First-order problem
34A55
semigroup
Second-order problem
Periodic solution
Inverse problem
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PublicationTitle Annali dell'Università di Ferrara. Sezione 7. Scienze matematiche
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Springer Nature B.V
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References Al HoraniMFaviniAPerturbation method for first- and complete second-order differential equationsJ. Optim. Theory Appl.2015130949967337560910.1007/s10957-015-0733-9
EidelmanYSTikhonovIVOn periodic solutions of abstract differential equationsAbstr. Appl. Anal.201168489499188099010.1155/S1085337501000537
Al Horani, M., Favini, A.: Inverse problems for control theory. In: Barbu, V., Lefter, C., Vrabie, I.I. (eds.) The 8th Congress of Romanian Mathematicians: New Trends in Differential Equations, Control Theory and Optimization, pp. 173–183 (2015)
LunardiAInterpolation Theory2009PisaScuola Normale Superiore1171.41001
Al HoraniMFaviniATanabeHParabolic first and second order differential equationsMilan J. Math.2016842299315357459810.1007/s00032-016-0260-7
FaviniALorenziATanabeHSingular integro-differential equations of parabolic typeAdv. Diff. Equ.20027776979818951651033.45010
BarbuVFaviniAPeriodic solutions for degenerate differential equationsRend. Istit. Mat. Univ. Trieste19972829570916.34042
LizamaCMild almost periodic solutions of abstract differential equationsJ. Math. Anal. Appl.19891432560571102255510.1016/0022-247X(89)90060-7
FaviniAYagiADegenerate Differential Equations in Banach Spaces1999New YorkMarcel Dekker. Inc.0913.34001
LionsJLPeetreJSur une classe d’espaces d’interpolationPubl. Math. de l’IHS19641956816534310.1007/BF02684796
ArendtWBattyCJKHieberMNeubranderFVector-valued Laplace Transforms and Cauchy Problems2011Birkhäuser, BaselMonographs in Mathematics10.1007/978-3-0348-0087-7
BurtonTAZhangBoPeriodic solutions of abstract differential equations with infinite delayJ. Diff. Equ.199190357396110124510.1016/0022-0396(91)90153-Z
Al HoraniMFaviniATanabeHInverse problems for evolution equations with time dependent operator-coefficientsDiscret. Contin. Dyn. Syst. Ser. S20169737744350363710.3934/dcdss.2016025
FaviniAYagiAMultivalued linear operators and degenerate evolution equationsAnn. Mat. Pura Appl.19931631353384121960510.1007/BF01759029
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TA Burton (303_CR7) 1991; 90
M Al Horani (303_CR4) 2015; 130
JL Lions (303_CR12) 1964; 19
C Lizama (303_CR13) 1989; 143
YS Eidelman (303_CR8) 2011; 6
A Favini (303_CR11) 1993; 163
A Favini (303_CR10) 1999
303_CR14
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M Al Horani (303_CR2) 2016; 84
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A Favini (303_CR9) 2002; 7
M Al Horani (303_CR3) 2016; 9
V Barbu (303_CR6) 1997; 28
A Lunardi (303_CR15) 2009
W Arendt (303_CR5) 2011
References_xml – reference: Al HoraniMFaviniATanabeHInverse problems for evolution equations with time dependent operator-coefficientsDiscret. Contin. Dyn. Syst. Ser. S20169737744350363710.3934/dcdss.2016025
– reference: Al Horani, M., Favini, A.: Inverse problems for control theory. In: Barbu, V., Lefter, C., Vrabie, I.I. (eds.) The 8th Congress of Romanian Mathematicians: New Trends in Differential Equations, Control Theory and Optimization, pp. 173–183 (2015)
– reference: LizamaCMild almost periodic solutions of abstract differential equationsJ. Math. Anal. Appl.19891432560571102255510.1016/0022-247X(89)90060-7
– reference: FaviniAYagiAMultivalued linear operators and degenerate evolution equationsAnn. Mat. Pura Appl.19931631353384121960510.1007/BF01759029
– reference: LunardiAInterpolation Theory2009PisaScuola Normale Superiore1171.41001
– reference: BurtonTAZhangBoPeriodic solutions of abstract differential equations with infinite delayJ. Diff. Equ.199190357396110124510.1016/0022-0396(91)90153-Z
– reference: FaviniAYagiADegenerate Differential Equations in Banach Spaces1999New YorkMarcel Dekker. Inc.0913.34001
– reference: Lizama, C., Ponce, R.: Periodic solutions of degenerate differential equations in vector-valued function spaces (preprint)
– reference: Al HoraniMFaviniAPerturbation method for first- and complete second-order differential equationsJ. Optim. Theory Appl.2015130949967337560910.1007/s10957-015-0733-9
– reference: EidelmanYSTikhonovIVOn periodic solutions of abstract differential equationsAbstr. Appl. Anal.201168489499188099010.1155/S1085337501000537
– reference: FaviniALorenziATanabeHSingular integro-differential equations of parabolic typeAdv. Diff. Equ.20027776979818951651033.45010
– reference: LionsJLPeetreJSur une classe d’espaces d’interpolationPubl. Math. de l’IHS19641956816534310.1007/BF02684796
– reference: Thanh Lan, N.: Operator Equation AX - BXD = C and Degenerate Differential Equations in Banach Spaces (preprint)
– reference: Al HoraniMFaviniATanabeHParabolic first and second order differential equationsMilan J. Math.2016842299315357459810.1007/s00032-016-0260-7
– reference: BarbuVFaviniAPeriodic solutions for degenerate differential equationsRend. Istit. Mat. Univ. Trieste19972829570916.34042
– reference: ArendtWBattyCJKHieberMNeubranderFVector-valued Laplace Transforms and Cauchy Problems2011Birkhäuser, BaselMonographs in Mathematics10.1007/978-3-0348-0087-7
– volume: 19
  start-page: 5
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  ident: 303_CR12
  publication-title: Publ. Math. de l’IHS
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  doi: 10.3934/dcdss.2016025
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  doi: 10.1007/s00032-016-0260-7
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  publication-title: Abstr. Appl. Anal.
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  publication-title: J. Optim. Theory Appl.
  doi: 10.1007/s10957-015-0733-9
– volume: 28
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  publication-title: Rend. Istit. Mat. Univ. Trieste
– volume-title: Degenerate Differential Equations in Banach Spaces
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– volume: 90
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  publication-title: J. Diff. Equ.
  doi: 10.1016/0022-0396(91)90153-Z
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Snippet We are concerned with a general abstract equation that allows to handle various degenerate first and second order differential equations in Banach spaces. We...
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SubjectTerms Algebraic Geometry
Analysis
Banach spaces
Geometry
History of Mathematical Sciences
Inverse problems
Mathematical analysis
Mathematics
Mathematics and Statistics
Nondestructive testing
Numerical Analysis
Partial differential equations
Title Direct and inverse problems for degenerate differential equations
URI https://link.springer.com/article/10.1007/s11565-018-0303-9
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