Determining the source term in an abstract parabolic problem from a time integral of the solution

Authors

  • Davide Guidetti University of Bologna

DOI:

https://doi.org/10.6092/issn.2240-2829/2670

Abstract

Consideriamo il problema della ricostruzione del termine di sorgente in un'equazione astratta di tipo parabolico. L'informazione supplementare, necessaria per la determinazione della soluzione del sistema e della parte incognita del termine di sorgente, è data dalla conoscenza di un integrale della soluzione rispetto alla variabile temporale e a una certa misura di Borel. Presento un teorema di esistenza e unicità di una soluzione, che è anche di regolarità massimale. Esamino alcuni casi particolari, assieme al fatto che talvolta il problema gode di una sorta di proprietà dell'alternativa di Fredholm.

References

Y. E. Anikonov, A. Lorenzi, "Explicit representation for the solution to a parabolic differential identication problem in a Banach space", J. Inv. Ill-Posed Problems 15 (2007), 669-681.

D. Guidetti, "On interpolation with boundary conditions", Math. Z. 207 (1991), 439-460.

D. Guidetti, "Determining the Source Term in an abstract parabolic Problem from a Time Integral of the Solution", to appear in Med. J. Math..

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.

T. Kato, A Short Introduction to Perturbation Theory for Linear Operators, Springer-Verlag (1982).

A. Lorenzi, A. I. Prilepko, "Fredholm-type results for integrodifferential identication parabolic problems", Dierential Integral Equations 6 (1993), 535-552.

A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhauser (1995).

A. I. Prilepko, A. B. Kostin, "An estimate for the spectral radius of an operator and the solvability of inverse problems for evolution equation", Math. Notes 53 (1993), 63-66.

A. I. Prilepko, D. G. Orlovsky, I. A. Vasin, Methods for solving inverse problems in mathematical physics, Marcel Dekker (1999).

A. I. Prilepko, S. Piskarev, S.-Y. Shaw, "On approximation of inverse problems for abstract parabolic dierential equations in Banach spaces", J. Inverse IllPosed Probl. 15 (2007), 831-851.

A. I. Prilepko, I. V. Tikhonov, "Recovery of the nonhomogeneous term in an abstract evolution equation", Russian Acad. Sc. Izv. Math. 44 (1995), 373-394.

F. Riesz, B. Sz.-Nagy, Lecons d'analyse fonctionelle, Academie des Sciences de Hongrie (1952).

W. Rundell, "Determination of an unknown nonhomogeneous term in a linear partial differential equation from overspecied boundary data", Applicable Anal. 10 (1980), 231-242.

A. E. Taylor, Introduction to functional Analysis, Chapman & Hall (1958).

I. V. Tikhonov, Y. S. Eidel'man, "Uniqueness of the solution of a two-point inverse problem for an abstract differential equation with an unknown parameter", Di er. Equ. Vol. 36 (2000), 1256-1258.

I. V. Tikhonov, Y. S. Eidel'man, "Spectral mapping theorems for point spectra for C0

Downloads

Published

2011-12-31

How to Cite

Guidetti, D. (2011). Determining the source term in an abstract parabolic problem from a time integral of the solution. Bruno Pini Mathematical Analysis Seminar, 2(1). https://doi.org/10.6092/issn.2240-2829/2670

Issue

Section

Articles