@article{VYURU_2015_8_3_a5,
author = {F. Colombo},
title = {On some methods to solve integrodifferential inverse problems of parabolic type},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
pages = {95--115},
year = {2015},
volume = {8},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VYURU_2015_8_3_a5/}
}
TY - JOUR AU - F. Colombo TI - On some methods to solve integrodifferential inverse problems of parabolic type JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie PY - 2015 SP - 95 EP - 115 VL - 8 IS - 3 UR - http://geodesic.mathdoc.fr/item/VYURU_2015_8_3_a5/ LA - en ID - VYURU_2015_8_3_a5 ER -
%0 Journal Article %A F. Colombo %T On some methods to solve integrodifferential inverse problems of parabolic type %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2015 %P 95-115 %V 8 %N 3 %U http://geodesic.mathdoc.fr/item/VYURU_2015_8_3_a5/ %G en %F VYURU_2015_8_3_a5
F. Colombo. On some methods to solve integrodifferential inverse problems of parabolic type. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 3, pp. 95-115. http://geodesic.mathdoc.fr/item/VYURU_2015_8_3_a5/
[1] Colombo F., Lorenzi A., “Identification of Time and Space Dependent Relaxation Kernels in the Theory of Materials with Memory, I”, J. Math. Anal. Appl., 213 (1997), 32–62 | DOI | MR | Zbl
[2] Colombo F., Lorenzi A., “Identification of Time and Space Dependent Relaxation Kernels in the Theory of Materials with Memory, II”, J. Math. Anal. Appl., 213 (1997), 63–90 | DOI | MR | Zbl
[3] Colombo F., Lorenzi A., “An Identification Problem Related to a Parabolic Integrodifferential Equation with Noncommuting Spatial Operators”, J. Inverse Ill-Posed Probl., 8 (2000), 505–540 | DOI | MR | Zbl
[4] Colombo F., Guidetti D., Lorenzi A., “Integrodifferential Identification Problems for the Heat Equation in Cylindrical Domains”, Adv. Math. Sci. Appl., 13 (2003), 639–662 | MR | Zbl
[5] Colombo F., Guidetti D., Lorenzi A., “Integrodifferential Identification Problems for Thermal Materials with Memory in Non-Smooth Plane Domains”, Dyn. Syst. Appl., 12 (2003), 533–560 | MR
[6] Lorenzi A., Direct and Inverse Integrodifferential Maxwell Problems for Dispersive Media Related to Cylindrical Domains, SIAM, Philadelphia, 1995 | MR | Zbl
[7] Di Cristo M., Guidetti D., Lorenzi A., “Abstract Parabolic Equations with Applications to Problems in Cylindrical Space Domains”, Adv. Differential Equations, 15 (2010), 1–42 | MR | Zbl
[8] Colombo F., “Direct and Inverse Problems for a Phase-Field Model with Memory”, J. Math. Anal. Appl., 260 (2001), 517–545 | DOI | MR | Zbl
[9] Lorenzi A., Rocca E., “Identification of Two Memory Kernels in a Fully Hyperbolic Phase-Field System”, J. Inverse Ill-Posed Probl., 16 (2008), 147–174 | DOI | MR | Zbl
[10] Lorenzi A., “An Identification Problem for a Conserved Phase-Field Model with Memory”, Math. Methods Appl. Sci., 28 (2005), 1315–1339 | DOI | MR | Zbl
[11] Guidetti D., Lorenzi A., “A Mixed Type Identification Problem Related to a Phase-field Model with Memory”, Osaka J. Math., 44 (2007), 579–613 | MR | Zbl
[12] Colombo F., Guidetti D., Lorenzi A., “Identification of Two Memory Kernels and the Time Dependence of the Heat Source for a Parabolic Conserved Phase-Field Model”, Math. Meth. Appl. Sci., 28 (2006), 2085–2115 | DOI | MR
[13] Colombo F., Lorenzi A., “An Inverse Problem in the Theory of Combustion of Materials with Memory”, Adv. Differential Equations, 3 (1998), 133–154 | MR | Zbl
[14] Colombo F., “An Inverse Problem for a Parabolic Integrodifferential Model in the Theory of Combustion”, Physica D, 236 (2007), 81–89 | DOI | MR | Zbl
[15] Colombo F., Guidetti D., “A Unified Approach to Nonlinear Integrodifferential Inverse Problems of Parabolic Type”, Z. Anal. Anwendungen, 21 (2002), 431–464 | DOI | MR | Zbl
[16] Colombo F., “An Inverse Problem for the Strongly Damped Wave Equation with Memory”, Nonlinearity, 20 (2007), 659–683 | DOI | MR | Zbl
[17] Colombo F., Guidetti D., “Identification of the Memory Kernel in the Strongly Damped Wave Equation by a Flux Condition”, Commun. Pure Appl. Anal., 8 (2009), 601–620 | DOI | MR | Zbl
[18] Bakushinsky A. B., Kokurin M. Yu., Iterative Methods for Approximate Solution of Inverse Problems, Springer, Dordrecht, 2004 | MR | Zbl
[19] Bertero M., Boccacci P., Introduction to Inverse Problems in Imaging, Institute of Physics Publishing, Bristol, 1998 | DOI | MR | Zbl
[20] Groetsch C. W., Inverse Problems. Activities for Undergraduates, Mathematical Association of America, Washington, 1999 | MR | Zbl
[21] Gladwell G. M. L., Inverse Problems in Vibration, Kluwer Academic Publishers, Dordrecht, 2004 | MR
[22] Kabanikhin S. I., Lorenzi A., Identification Problems of Wave Phenomena, Theory and Numerics, VSP, Utrecht, 1999 | MR
[23] Isakov V., Inverse Problems for Partial Differential Equations, Springer-Verlag, New York, 1998 | DOI | MR | Zbl
[24] Kirsch A., An Introduction to the Mathematical Theory of Inverse Problems, Springer-Verlag, New York, 1996 | DOI | MR | Zbl
[25] Kaipio J., Somersalo E., Statistical and Computational Inverse Problems, Springer-Verlag, New York, 2005 | MR | Zbl
[26] Prilepko A. I., Orlovsky D. G., Vasin I. A., Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker, Inc., New York, 2000 | MR | Zbl
[27] Romanov V. G., Investigation Methods for Inverse Problems, VSP, Utrecht, 2002 | DOI | MR | Zbl
[28] Colombo F., Guidetti D., “An Inverse Problem for a Phase-Field Model in Sobolev Spaces”, Progress in Nonlinear Differential Equations and Their Applications, 64 (2005), 189–210 | DOI | MR | Zbl
[29] Colombo F., Guidetti D., “A Global in Time Existence and Uniqueness Result for a Semilinear Integrodifferential Parabolic Inverse Problem in Sobolev Spaces”, Math. Models Methods Appl. Sci., 17 (2007), 1–29 | DOI | MR
[30] Lunardi A., Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhauser Verlag, Basel, 1995 | MR | Zbl
[31] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag der Wissenschaften, Berlin, 1978 | MR | Zbl
[32] Triebel H., Theory of Functions Spaces, Birkhauser Verlag, Basel, 1983 | DOI | MR
[33] Adams R., Sobolev Spaces, Academic Press, New York, 1975 | MR | Zbl
[34] Dore G., “Maximal Regularity in $L^p$ Spaces for an Abstract Cauchy Problem”, Adv. Diff. Eq., 5 (2000), 293–322 | MR | Zbl
[35] Hillen T., “Qualitative Analysis of Semilinear Cattaneo Equations”, Math. Models Methods Appl. Sci., 8 (1998), 507–519 | DOI | MR | Zbl