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Classical solutions to quasilinear parabolic problems with dynamic boundary conditions
Inverse problems for evolution equations with time dependent operator-coefficients
| 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 |
| 3. | Hirai Sanso 12-13, Takarazuka 665-0817 |
References:
| [1] |
P. Acquistapace, A unified approach to abstract linear nonautonomous parabolic equations, Rend. Sem. Mat.Univ. Padova, 78 (1987), 47-107. |
| [2] |
M. Al Horani and A. Favini, Degenerate first-order identification problems in Banach spaces, in Differential equations: inverse and direct problems (eds. A. Favini and A. Lorenzi), Taylor and Francis Group, 251 (2006), 1-15.
doi: 10.1201/9781420011135.ch1. |
| [3] |
M. Al Horani and A. Favini, An identification problem for first-order degenerate differential equations, J. Optim. Theory Appl., 130 (2006), 41-60.
doi: 10.1007/s10957-006-9083-y. |
| [4] |
M. Al Horani and A. Favini, Degenerate first-order inverse problems in Banach spaces, Nonlinear Anal., 75 (2012), 68-77.
doi: 10.1016/j.na.2011.08.001. |
| [5] |
M. Al Horani and A. Favini, First-order inverse evolution equations, Evol. Equ. Control Theory, 3 (2014), 355-361.
doi: 10.3934/eect.2014.3.355. |
| [6] |
M. Al Horani and A. Favini, Inverse problems for singular differential-operator equations with higher order polar singularities, Discrete. Contin. Dyn. Syst. Ser. B, 19 (2014), 2159-2168.
doi: 10.3934/dcdsb.2014.19.2159. |
| [7] |
M. Al Horani and A. Favini, Perturbation method for first and complete second order differential equations, J. Optim. Theory Appl., 166 (2015), 949-967.
doi: 10.1007/s10957-015-0733-9. |
| [8] |
H. Amann, Linear and Quasilinear Parabolic Problems. Vol. I. Abstract Linear Theory, Monographs in Mathematics, 89, Birkhauser, Basel-Borton-Berlin, 1995.
doi: 10.1007/978-3-0348-9221-6. |
| [9] |
S. Bertoni, Stability of CD-systems under perturbations in the Favard class, Mediterr. J. Math., 11 (2014), 1195-1204.
doi: 10.1007/s00009-013-0376-8. |
| [10] |
A. Favini and A. Lorenzi, Identification problems for singular integro-differential equations of parabolic type I, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 12 (2005), 303-328. |
| [11] |
A. Favini and A. Lorenzi, Identification problems in singular integro-differential equations of parabolic type II, Nonlinear Anal., 56 (2004), 879-904.
doi: 10.1016/j.na.2003.10.018. |
| [12] |
A. Favini, A. Lorenzi, G. Marinoschi and H. Tanabe, Perturbation methods and identification problems for degenerate evolution systems, Advances in mathematics, Ed. Acad. Române, Bucharest, (2013), 145-156. |
| [13] |
A. Favini, A. Lorenzi and H. Tanabe, Direct and inverse problems for systems of singular differential boundary-value problems, Electron. J. Differential Equations, 225 (2012), 1-34. |
| [14] |
A. Favini, A. Lorenzi and H. Tanabe, First-order regular and degenerate identification differential problems, Abstr. Appl. Anal., (2015), Art. ID 393624, 42 pp.
doi: 10.1155/2015/393624. |
| [15] |
A. Favini, A. Lorenzi and H. Tanabe, Degenerate integro-differential equations of parabolic type with Robin boundary conditions, submitted. |
| [16] |
A. Favini, A. Lorenzi and H. Tanabe, Direct and inverse degenerate parabolic differential equations with multi-valued operators, Electron. J. Diff. Equ., 2015 (2015), 1-22. |
| [17] |
A. Favini and G. Marinoschi, Identification of the time derivative coefficient in a fast diffusion degenerate equation, J. Optim. Theory Appl., 145 (2010), 249-269.
doi: 10.1007/s10957-009-9635-z. |
| [18] |
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. |
| [19] |
A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc. New York, 1999. |
| [20] |
A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
| [21] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differntial Equations, Applied Mathematical Sciences 44, Springer, Berlin, 1983.
doi: 10.1007/978-1-4612-5561-1. |
| [22] |
A.I. Prilepko, D.G. Orlovsky and I.A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker. Inc. New York, 2000. |
| [23] |
H, Tanabe, Functional Analytic Methods for Partial Differential Equations, Monographs and Textbooks in Pure and Applied Mathematics 204, Marcel Dekker, Inc. New York, 1997. |
show all references
References:
| [1] |
P. Acquistapace, A unified approach to abstract linear nonautonomous parabolic equations, Rend. Sem. Mat.Univ. Padova, 78 (1987), 47-107. |
| [2] |
M. Al Horani and A. Favini, Degenerate first-order identification problems in Banach spaces, in Differential equations: inverse and direct problems (eds. A. Favini and A. Lorenzi), Taylor and Francis Group, 251 (2006), 1-15.
doi: 10.1201/9781420011135.ch1. |
| [3] |
M. Al Horani and A. Favini, An identification problem for first-order degenerate differential equations, J. Optim. Theory Appl., 130 (2006), 41-60.
doi: 10.1007/s10957-006-9083-y. |
| [4] |
M. Al Horani and A. Favini, Degenerate first-order inverse problems in Banach spaces, Nonlinear Anal., 75 (2012), 68-77.
doi: 10.1016/j.na.2011.08.001. |
| [5] |
M. Al Horani and A. Favini, First-order inverse evolution equations, Evol. Equ. Control Theory, 3 (2014), 355-361.
doi: 10.3934/eect.2014.3.355. |
| [6] |
M. Al Horani and A. Favini, Inverse problems for singular differential-operator equations with higher order polar singularities, Discrete. Contin. Dyn. Syst. Ser. B, 19 (2014), 2159-2168.
doi: 10.3934/dcdsb.2014.19.2159. |
| [7] |
M. Al Horani and A. Favini, Perturbation method for first and complete second order differential equations, J. Optim. Theory Appl., 166 (2015), 949-967.
doi: 10.1007/s10957-015-0733-9. |
| [8] |
H. Amann, Linear and Quasilinear Parabolic Problems. Vol. I. Abstract Linear Theory, Monographs in Mathematics, 89, Birkhauser, Basel-Borton-Berlin, 1995.
doi: 10.1007/978-3-0348-9221-6. |
| [9] |
S. Bertoni, Stability of CD-systems under perturbations in the Favard class, Mediterr. J. Math., 11 (2014), 1195-1204.
doi: 10.1007/s00009-013-0376-8. |
| [10] |
A. Favini and A. Lorenzi, Identification problems for singular integro-differential equations of parabolic type I, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 12 (2005), 303-328. |
| [11] |
A. Favini and A. Lorenzi, Identification problems in singular integro-differential equations of parabolic type II, Nonlinear Anal., 56 (2004), 879-904.
doi: 10.1016/j.na.2003.10.018. |
| [12] |
A. Favini, A. Lorenzi, G. Marinoschi and H. Tanabe, Perturbation methods and identification problems for degenerate evolution systems, Advances in mathematics, Ed. Acad. Române, Bucharest, (2013), 145-156. |
| [13] |
A. Favini, A. Lorenzi and H. Tanabe, Direct and inverse problems for systems of singular differential boundary-value problems, Electron. J. Differential Equations, 225 (2012), 1-34. |
| [14] |
A. Favini, A. Lorenzi and H. Tanabe, First-order regular and degenerate identification differential problems, Abstr. Appl. Anal., (2015), Art. ID 393624, 42 pp.
doi: 10.1155/2015/393624. |
| [15] |
A. Favini, A. Lorenzi and H. Tanabe, Degenerate integro-differential equations of parabolic type with Robin boundary conditions, submitted. |
| [16] |
A. Favini, A. Lorenzi and H. Tanabe, Direct and inverse degenerate parabolic differential equations with multi-valued operators, Electron. J. Diff. Equ., 2015 (2015), 1-22. |
| [17] |
A. Favini and G. Marinoschi, Identification of the time derivative coefficient in a fast diffusion degenerate equation, J. Optim. Theory Appl., 145 (2010), 249-269.
doi: 10.1007/s10957-009-9635-z. |
| [18] |
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. |
| [19] |
A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc. New York, 1999. |
| [20] |
A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
| [21] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differntial Equations, Applied Mathematical Sciences 44, Springer, Berlin, 1983.
doi: 10.1007/978-1-4612-5561-1. |
| [22] |
A.I. Prilepko, D.G. Orlovsky and I.A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker. Inc. New York, 2000. |
| [23] |
H, Tanabe, Functional Analytic Methods for Partial Differential Equations, Monographs and Textbooks in Pure and Applied Mathematics 204, Marcel Dekker, Inc. New York, 1997. |
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