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Original Articles

On a Finite Difference Scheme for an Inverse Integro-Differential Problem Using Semigroup Theory: A Functional Analytic Approach

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Pages 850-886 | Received 30 Dec 2015, Accepted 17 Apr 2016, Published online: 22 Apr 2016

References

  • A. Ashyraliev and P. E. Sobolevskii (1994). Well-posedness of parabolic difference equations. Operator Theory Advances and Applications 69.
  • J. Bergh and J. Löfström (1976). Interpolation Spaces. An Introduction. Number 223 in Grundlehren der mathematischen Wissenschaften. Springer, Berlin, Germany.
  • Cecilia Cavaterra and D. Guidetti (2015). Identification of a source factor in a control problem for the heat equation with a boundary memory term. Mathematical Methods in the Applied Sciences 38(18):4818–4839.
  • F. Colombo (2007). An inverse problem for a parabolic integrodifferential model in the theory of combustion. Physica D 236:81–89.
  • F. Colombo (2007). An inverse problem for the strongly damped wave equation with memory. Nonlinearity 20:659–683.
  • F. Colombo and D. Guidetti (2002). Unified approach to nonlinear integro-differential inverse problems of parabolic type. Zeitschrift für Analysis und ihre Anwendungen 21:431–464.
  • F. Colombo and D. Guidetti (2007). A global in time existence and uniqueness result for a semilinear integrodifferentila parabolic inverse problem in Sobolev spaces. Mathematical Models and Methods in Applied Sciences 17(4):537–565.
  • F. Colombo and D. Guidetti (2008). An inverse problem for the beam equation with memory with nonhomogeneous boundary conditions. Inverse Problems 24(6):065015.
  • F. Colombo and D. Guidetti (2009). Identification of the memory kernel in the strongly damped wave equation by a flux condition. Communications on Pure and Applied Analysis 8:601–620.
  • F. Colombo and D. Guidetti (2011). Some results on the identification of memory kernels. In (M. Ruzhansky and J. Wirth eds.) Operator Theory: Advances and Applications 216, pages 121–138. Basel, Germany: Birkhäuser.
  • E. Davies (1980). One-Parameter Semigroups. Academic Press, London, United Kingdom.
  • L. de Simon (1964). Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordiìne (An application of singular integration theory in linear partial differential equations of first order). Rendiconti del Seminario Matematico della Università di Padova 34:205–223.
  • R. H. de Staelen and M. Slodička (2015). Reconstruction of a convolution kernel in a semilinear parabolic problem based on a global measurement. Nonlinear Analysis Series A: Theory, Methods & Applications 112:43–57.
  • R. H. de Staelen, K. Van Bockstal, and M. Slodička (2015). Error analysis in the reconstruction of a convolution kernel in a semilinear parabolic problem. Journal of Computational and Applied Mathematics 275:382–391.
  • I. Faragó and J. Karátson (2002). Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators: Theory and Applications. Volume 11 of Advances in Compuation: Theory and Practice. Nova Science Publishers, Inc., New York, USA.
  • D. Guidetti (1991). On elliptic problems in Besov spaces. Mathematische Nachrichten 152:247–275.
  • D. Guidetti (1991). On interpolation with boundary conditions. Mathematische Zeitschrift 207(3):439–460.
  • D. Guidetti (2010). Reconstruction of a bounded variation convolution kernel in an abstract wave equation. Forum Mathematicum 22(6):1129–1160.
  • D. Guidetti and A. Lorenzi (2007). A mixed type identification problem related to a phase-field model with memory. Osaka Journal of Mathematics 44(3):579–613.
  • J. Kačur (1985). Method of Rothe in evolution equations. Teubner-Texte zur Mathematik.
  • A. Lorenzi and E. Sinestrari (1988). An inverse problem in the theory of materials with memory. Nonlinear Analysis 12:1317–1335.
  • K. Rektorys (1982). The Method of Discretization in Time and Partial Differential Equations (Transl. From the Czech By the Author.) In Mathematics and Its Applications (East European Series), Volume 4. Springer, The Netherlands..
  • J. Simon (1990). Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval. Annali di Matematica Pura ed Applicata 157:117–148.
  • K. Van Bockstal, R. H. De Staelen, and M. Slodička (2015). Identification of a memory kernel in a semilinear integrodifferential parabolic problem with applications in heat conduction with memory. Journal of Computational and Applied Mathematics 289:196–207.

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