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Partial reconstruction of the source term in a linear parabolic initial problem with Dirichlet boundary conditions
| 1. | Dipartimento di Matematica, Piazza di Porta S. Donato, 5, 40126 Bologna |
References:
| [1] |
P. Acquistapace and B. Terreni, Hölder classes with boundary conditions as interpolation spaces, Math. Z., 195 (1987), 451-471.
doi: 10.1007/BF01166699. |
| [2] |
H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Math. Nachr., 186 (1997), 5-56.
doi: 10.1002/mana.3211860102. |
| [3] |
H. Amann, Vector-Valued Distributions and Fourier Multipliers, manuscript (2003), University of Zürich. |
| [4] |
Y. E. Anikonov and A. Lorenzi, Explicit representation for the solution to a parabolic differential identification problem in a Banach space, J. Inv. Ill-Posed Problems, 15 (2007), 669-681.
doi: 10.1515/jiip.2007.037. |
| [5] |
Y. Y. Belov, "Inverse problems for Partial Differential Equations," Inverse Ill-posed Probl. Ser., VSP, 2002.
doi: 10.1515/9783110944631. |
| [6] |
M. Di Cristo, D. Guidetti and A. Lorenzi, Abstract parabolic equations with applications to problems in cylindrical space domains, Adv. Diff. Eq., 15 (2010), 1-42. |
| [7] |
P. Grisvard, Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures et appl., 45 (1966), 143-206. |
| [8] |
P. Grisvard, Spazi di tracce e applicazioni, Rend. Mat., 6 (1972), 657-729. |
| [9] |
D. Guidetti, On interpolation with boundary conditions, Math. Z., 207 (1991), 439-460.
doi: 10.1007/BF02571401. |
| [10] |
D. Guidetti, The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are Hölder continuous with respect to space variables, Rend. Mat. Acc. Lincei, 7 (1996), 161-168. |
| [11] |
D. Guidetti, Partial reconstruction of the source term in a linear parabolic initial problem with first order boundary conditions, to appear in Applicable Analysis (2013). |
| [12] |
D. Guidetti and S. Piskarev, On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems, Abstr. Appl. Anal., 18 (2003), 1005-1035.
doi: 10.1155/S1085337503306359. |
| [13] |
A. Hasanov, Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solutions approach, J. Math. Anal. Appl., 330 (2007), 766-779.
doi: 10.1016/j.jmaa.2006.08.018. |
| [14] |
N. V. Krylov, "Lectures on Elliptic and Parabolic Equations in Hölder Spaces," Graduate Studies in Mathematics vol. 12, American Mathematical Society, 1996. |
| [15] |
A. Lorenzi and A. I. Prilepko, Fredholm-type results for integrodifferential identification parabolic problems, Differential Integral Equations, 6 (1993), 535-552. |
| [16] |
A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems" Birkhäuser, 1995.
doi: 10.1007/978-3-0348-9234-6. |
| [17] |
A. I. Prilepko, D. G. Orlovsky and I. A. Vasin, "Methods for Solving Inverse Problems in Mathematical Physics," Marcel Dekker, 1999. |
| [18] |
W. Rundell, Determination of an unknown nonhomogeneous term in a linear partial differential equation from overspecified boundary data, Applicable Anal., 10 (1980), 231-242.
doi: 10.1080/00036818008839304. |
| [19] |
L. Schwartz, "Mixed Problems in Partial Differential Equations and Representations of Semigroups," Tata Institute of Fundamental Research, 1964. |
| [20] |
B. Stewart, Generation of analytic semigroups by strongly elliptic operators, Trans. Am. Math. Soc., 199 (1974), 141-162.
doi: 10.1090/S0002-9947-1974-0358067-4. |
| [21] |
H. Tanabe, "Equations of Evolution," Pitman, 1979. |
| [22] |
W. von Wahl, Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Rumen hölderstetiger Funktionen, Nachr. Akad. Wiss. Göttingen II, Math. Phys. Klasse Jahrgang, 11 (1972), 231-258. |
show all references
References:
| [1] |
P. Acquistapace and B. Terreni, Hölder classes with boundary conditions as interpolation spaces, Math. Z., 195 (1987), 451-471.
doi: 10.1007/BF01166699. |
| [2] |
H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Math. Nachr., 186 (1997), 5-56.
doi: 10.1002/mana.3211860102. |
| [3] |
H. Amann, Vector-Valued Distributions and Fourier Multipliers, manuscript (2003), University of Zürich. |
| [4] |
Y. E. Anikonov and A. Lorenzi, Explicit representation for the solution to a parabolic differential identification problem in a Banach space, J. Inv. Ill-Posed Problems, 15 (2007), 669-681.
doi: 10.1515/jiip.2007.037. |
| [5] |
Y. Y. Belov, "Inverse problems for Partial Differential Equations," Inverse Ill-posed Probl. Ser., VSP, 2002.
doi: 10.1515/9783110944631. |
| [6] |
M. Di Cristo, D. Guidetti and A. Lorenzi, Abstract parabolic equations with applications to problems in cylindrical space domains, Adv. Diff. Eq., 15 (2010), 1-42. |
| [7] |
P. Grisvard, Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures et appl., 45 (1966), 143-206. |
| [8] |
P. Grisvard, Spazi di tracce e applicazioni, Rend. Mat., 6 (1972), 657-729. |
| [9] |
D. Guidetti, On interpolation with boundary conditions, Math. Z., 207 (1991), 439-460.
doi: 10.1007/BF02571401. |
| [10] |
D. Guidetti, The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are Hölder continuous with respect to space variables, Rend. Mat. Acc. Lincei, 7 (1996), 161-168. |
| [11] |
D. Guidetti, Partial reconstruction of the source term in a linear parabolic initial problem with first order boundary conditions, to appear in Applicable Analysis (2013). |
| [12] |
D. Guidetti and S. Piskarev, On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems, Abstr. Appl. Anal., 18 (2003), 1005-1035.
doi: 10.1155/S1085337503306359. |
| [13] |
A. Hasanov, Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solutions approach, J. Math. Anal. Appl., 330 (2007), 766-779.
doi: 10.1016/j.jmaa.2006.08.018. |
| [14] |
N. V. Krylov, "Lectures on Elliptic and Parabolic Equations in Hölder Spaces," Graduate Studies in Mathematics vol. 12, American Mathematical Society, 1996. |
| [15] |
A. Lorenzi and A. I. Prilepko, Fredholm-type results for integrodifferential identification parabolic problems, Differential Integral Equations, 6 (1993), 535-552. |
| [16] |
A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems" Birkhäuser, 1995.
doi: 10.1007/978-3-0348-9234-6. |
| [17] |
A. I. Prilepko, D. G. Orlovsky and I. A. Vasin, "Methods for Solving Inverse Problems in Mathematical Physics," Marcel Dekker, 1999. |
| [18] |
W. Rundell, Determination of an unknown nonhomogeneous term in a linear partial differential equation from overspecified boundary data, Applicable Anal., 10 (1980), 231-242.
doi: 10.1080/00036818008839304. |
| [19] |
L. Schwartz, "Mixed Problems in Partial Differential Equations and Representations of Semigroups," Tata Institute of Fundamental Research, 1964. |
| [20] |
B. Stewart, Generation of analytic semigroups by strongly elliptic operators, Trans. Am. Math. Soc., 199 (1974), 141-162.
doi: 10.1090/S0002-9947-1974-0358067-4. |
| [21] |
H. Tanabe, "Equations of Evolution," Pitman, 1979. |
| [22] |
W. von Wahl, Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Rumen hölderstetiger Funktionen, Nachr. Akad. Wiss. Göttingen II, Math. Phys. Klasse Jahrgang, 11 (1972), 231-258. |
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