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Abstract and Applied Analysis
Volume 2015 (2015), Article ID 393624, 42 pages
http://dx.doi.org/10.1155/2015/393624
Research Article

First-Order Regular and Degenerate Identification Differential Problems

1Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
2Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy
3Hirai Sanso 12-13, Takarazuka 665-0817, Japan

Received 19 August 2013; Accepted 11 February 2014

Academic Editor: Baoxiang Wang

Copyright © 2015 A. Favini et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Al Horani and A. Favini, “An identification problem for first-order degenerate differential equations,” Journal of Optimization Theory and Applications, vol. 130, no. 1, pp. 41–60, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. Al-Horani and A. Favini, “Degenerate first order identification problems in Banach spaces,” in Differential Equations Inverse and Direct Problems, A. Favini and A. Lorenzi, Eds., pp. 1–15, Taylor & Francis, Boca Raton, Fla, USA, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker, New York, NY, USA, 1st edition, 1999. View at MathSciNet
  4. K. Engel, “Operator matrices and systems of evolution equations,” In press.
  5. A. Yagi, Abstract Parabolic Evolution Equations and Their Applications, Monographs in Mathematics, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  6. K. Taira, “The theory of semigroups with weak singularity and its applications to partial differential equations,” Tsukuba Journal of Mathematics, vol. 13, no. 2, pp. 513–562, 1989. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. V. Capasso and K. Kunisch, “A reaction-diffusion system arising in modelling man-environment diseases,” Quarterly of Applied Mathematics, vol. 46, no. 3, pp. 431–450, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Al Horani and A. Favini, “Degenerate first-order inverse problems in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 1, pp. 68–77, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, The Netherlands, 1978. View at MathSciNet
  10. W. von Wahl, “Lineare und semilineare parabolische Differentialgleichungen in Räumen hölderstetiger Funktionen,” Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 43, pp. 234–262, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. L. Lorenzi and M. Bertoldi, Analytic Methods for Markov Semigroups, vol. 283 of Pure and Applied Mathematics, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2007. View at MathSciNet
  12. I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximation Theories I, II: Abstract Parabolic Systems, Cambridge University Press, Cambridge, UK, 2000. View at MathSciNet
  13. K. Taira, Analytic Semigroups and Semilinear Initial Boundary Value Problems, Cambridge University Press, Cambridge, UK, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C. Wild, “Semi-groupes de croissance α<1 holomorphes,” Comptes Rendus de l'Académie des Sciences, vol. 285, no. 6, pp. A437–A440, 1977. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. Favini, A. Lorenzi, H. Tanabe, and A. Yagi, “An Lp-approach to singular linear parabolic equations in bounded domains,” Osaka Journal of Mathematics, vol. 42, no. 2, pp. 385–406, 2005. View at Google Scholar · View at MathSciNet
  16. A. Favini, A. Lorenzi, H. Tanabe, and A. Yagi, “An Lp-approach to singular linear parabolic equations with lower order terms,” Discrete and Continuous Dynamical Systems A, vol. 22, no. 4, pp. 989–1008, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  17. A. Favini, A. Lorenzi, and H. Tanabe, “Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: L2-theory,” Journal of the Mathematical Society of Japan, vol. 61, no. 1, pp. 133–176, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  18. S. G. Kreĭn, Linear Differential Equations in Banach Space, American Mathematical Society, Providence, RI, USA, 1971. View at MathSciNet
  19. E. Sinestrari, “On the abstract Cauchy problem of parabolic type in spaces of continuous functions,” Journal of Mathematical Analysis and Applications, vol. 107, no. 1, pp. 16–66, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, Switzerland, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  21. K. Yosida, Functional Analysis, Springer, Berlin, Germany, 2nd edition, 1969.
  22. H. O. Fattorini, The Cauchy Problem, vol. 18 of Encyclopedia of Mathematics and its Applications, Addison-Wesley, Reading, Mass, USA, 1983. View at MathSciNet
  23. A. Pazy, Semigroups of Linear Operators and Application to Partial Differential Equations, vol. 44 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  24. K. Taira, “On the existence of Feller semigroups with discontinuous coefficients. II,” Acta Mathematica Sinica (English Series), vol. 25, no. 5, pp. 715–740, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. A. Favini, A. Lorenzi, and H. Tanabe, “Direct and inverse problems for systems of Singular differential boundary-value problems,” Electronic Journal of Differential Equations, vol. 2012, no. 255, pp. 1–34, 2012. View at Google Scholar