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Preface
First-order inverse evolution equations
| 1. | Department of Mathematics, The University of Jordan, Amman |
| 2. | Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna |
References:
| [1] |
M. Al Horani, An identification problem for some degenerate differential equations, Matematiche (Catania), 57 (2002), 217-227. |
| [2] |
M. Al Horani, Projection method for solving degenerate first-order identification problem, J. Math. Anal. Appl., 364 (2010), 204-208.
doi: 10.1016/j.jmaa.2009.10.033. |
| [3] |
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. |
| [4] |
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.
doi: 10.1201/9781420011135.ch1. |
| [5] |
M. Al Horani and A. Favini, Perturbation method for first and complete second order differential equations, Preprint. |
| [6] |
W. Desch and W. Schappacher, On relatively bounded perturbations of linear $C_0$-semigroups, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 11 (1984), 327-341. |
| [7] |
N. Dunford and T. Schwarz, Linear Operators, I, Wiley (Interscience), New York, 1958. |
| [8] |
K.-J. Engel and R. Nagel, One Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Math., Springer-Verlag, Berlin-Heidelgerg-New York, 2000. |
| [9] |
A. Favini and A. Lorenzi, Identification problems for singular integro-differential equations of parabolic type I, Dynamics of Continuous, Discrete and Impulsive Systems, Series A; Mathematical Analysis, 12 (2005), 303-328. |
| [10] |
A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc., New York, 1999. |
| [11] |
A. Favini and S. Romanelli, Analicity semigroups on $C[0,1]$ generated by some classes of second order differential equations, Semigroup Forum, 56 (1998), 362-372. |
| [12] |
G. Greiner, Spectral properties and asymptotic behavior of the linear transport equation, Math. Zeit., 185 (1984), 167-177.
doi: 10.1007/BF01181687. |
| [13] |
A. Lorenzi, An Introduction to Identification Problems Via Functional Analysis, VSP, Utrecht, The Netherland, 2001.
doi: 10.1515/9783110940923. |
| [14] |
A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, $1^{ist}$ ed, Birkhäuser, Basel, 1995. |
| [15] |
I. Prilepko, G. Orlovsky and A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker. Inc., New York, 2000. |
| [16] |
E. Sinestrari, Wave equation with memory, Discrete Contin. Dynam. Systems, 5 (1999), 881-896.
doi: 10.3934/dcds.1999.5.881. |
| [17] |
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amesterdam, 1978. |
show all references
References:
| [1] |
M. Al Horani, An identification problem for some degenerate differential equations, Matematiche (Catania), 57 (2002), 217-227. |
| [2] |
M. Al Horani, Projection method for solving degenerate first-order identification problem, J. Math. Anal. Appl., 364 (2010), 204-208.
doi: 10.1016/j.jmaa.2009.10.033. |
| [3] |
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. |
| [4] |
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.
doi: 10.1201/9781420011135.ch1. |
| [5] |
M. Al Horani and A. Favini, Perturbation method for first and complete second order differential equations, Preprint. |
| [6] |
W. Desch and W. Schappacher, On relatively bounded perturbations of linear $C_0$-semigroups, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 11 (1984), 327-341. |
| [7] |
N. Dunford and T. Schwarz, Linear Operators, I, Wiley (Interscience), New York, 1958. |
| [8] |
K.-J. Engel and R. Nagel, One Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Math., Springer-Verlag, Berlin-Heidelgerg-New York, 2000. |
| [9] |
A. Favini and A. Lorenzi, Identification problems for singular integro-differential equations of parabolic type I, Dynamics of Continuous, Discrete and Impulsive Systems, Series A; Mathematical Analysis, 12 (2005), 303-328. |
| [10] |
A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc., New York, 1999. |
| [11] |
A. Favini and S. Romanelli, Analicity semigroups on $C[0,1]$ generated by some classes of second order differential equations, Semigroup Forum, 56 (1998), 362-372. |
| [12] |
G. Greiner, Spectral properties and asymptotic behavior of the linear transport equation, Math. Zeit., 185 (1984), 167-177.
doi: 10.1007/BF01181687. |
| [13] |
A. Lorenzi, An Introduction to Identification Problems Via Functional Analysis, VSP, Utrecht, The Netherland, 2001.
doi: 10.1515/9783110940923. |
| [14] |
A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, $1^{ist}$ ed, Birkhäuser, Basel, 1995. |
| [15] |
I. Prilepko, G. Orlovsky and A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker. Inc., New York, 2000. |
| [16] |
E. Sinestrari, Wave equation with memory, Discrete Contin. Dynam. Systems, 5 (1999), 881-896.
doi: 10.3934/dcds.1999.5.881. |
| [17] |
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amesterdam, 1978. |
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