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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 180894, 17 pages
doi:10.1155/2012/180894
Research Article
Almost Periodic (Type) Solutions to Parabolic Cauchy Inverse Problems
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Received 23 December 2011; Revised 1 March 2012; Accepted 12 March 2012
Academic Editor: István Györi
Copyright © 2012 Fenglin Yang and Chuanyi Zhang. 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
- C. Y. Zhang, “Pseudo-almost-periodic solutions of some differential equations,” Journal of Mathematical Analysis and Applications, vol. 181, no. 1, pp. 62–76, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. Y. Zhang, “Integration of vector-valued pseudo-almost periodic functions,” Proceedings of the American Mathematical Society, vol. 121, no. 1, pp. 167–174, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- R. P. Agarwal, B. de Andrade, and C. Cuevas, “Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations,” Nonlinear Analysis, vol. 11, no. 5, pp. 3532–3554, 2010. View at Publisher · View at Google Scholar
- E. Ait Dads and O. Arino, “Exponential dichotomy and existence of pseudo almost-periodic solutions of some differential equations,” Nonlinear Analysis A, vol. 27, no. 4, pp. 369–386, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- E. Ait Dads and K. Ezzibi, “Positive pseudo almost periodic solutions for some nonlinear delay integrable equation,” J. Cybemetics, vol. 6, pp. 134–145, 1994.
- E. Ait Dads and K. Ezzinbi, “Pseudo almost periodic solutions of some delay differential equations,” Journal of Mathematical Analysis and Applications, vol. 201, no. 3, pp. 840–850, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- E. A. Dads and K. Ezzinbi, “Existence of positive pseudo-almost-periodic solution for some nonlinear infinite delay integral equations arising in epidemic problems,” Nonlinear Analysis A, vol. 41, pp. 1–13, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- E. Ait Dads, K. Ezzinbi, and O. Arino, “Pseudo almost periodic solutions for some differential equations in a Banach space,” Nonlinear Analysis A, vol. 28, no. 7, pp. 1141–1155, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. I. Alonso, J. Hong, and R. Obaya, “Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences,” Applied Mathematics Letters, vol. 13, no. 2, pp. 131–137, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. I. Alonso, J. Hong, and R. Obaya, “Exponential dichotomy and trichotomy for difference equations,” Computers & Mathematics with Applications, vol. 38, no. 1, pp. 41–49, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. I. Alonso, J. Hong, and J. Rojo, “A class of ergodic solutions of differential equations with piecewise constant arguments,” Dynamic Systems and Applications, vol. 7, no. 4, pp. 561–574, 1998. View at Zentralblatt MATH
- B. Basit and C. Zhang, “New almost periodic type functions and solutions of differential equations,” Canadian Journal of Mathematics, vol. 48, no. 6, pp. 1138–1153, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Hong and C. Núñez, “The almost periodic type difference equations,” Mathematical and Computer Modelling, vol. 28, no. 12, pp. 21–31, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Hong and R. Obaya, “Ergodic type solutions of some differential equations,” in Differential Equations and Nonlinear Mechanics, vol. 528, pp. 135–152, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001. View at Zentralblatt MATH
- J. Hong, R. Obaya, and A. S. Gil, “Exponential trichotomy and a class of ergodic solutions of differential equations with ergodic perturbations,” Applied Mathematics Letters, vol. 12, no. 1, pp. 7–13, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Hong, R. Obaya, and A. M. Sanz, “Ergodic solutions via ergodic sequences,” Nonlinear Analysis A, vol. 40, pp. 265–277, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Hong, R. Obaya, and A. Sanz, “Almost periodic type solutions of some differential equations with piecewise constant argument,” Nonlinear Analysis A, vol. 45, pp. 661–688, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- H.-X. Li, F.-I. Huang, and J.-Y. Li, “Composition of pseudo almost-periodic functions and semilinear differential equations,” Journal of Mathematical Analysis and Applications, vol. 255, no. 2, pp. 436–446, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- R. Yuan, “Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument,” Nonlinear Analysis A, vol. 41, pp. 871–890, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. Zhang, Almost Periodic Type Functions and Ergodicity, Science Press, Beijing, China, 2003.
- C. Y. Zhang, “Pseudo almost periodic solutions of some differential equations. II,” Journal of Mathematical Analysis and Applications, vol. 192, no. 2, pp. 543–561, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. Zhang, “Vector-valued pseudo almost periodic functions,” Czechoslovak Mathematical Journal, no. 3, pp. 385–394, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C.-Y. Zhang, “Ergodicity and its applications. I. Basic properties,” Acta Analysis Functionalis Applicata, vol. 1, no. 1, pp. 28–39, 1999. View at Zentralblatt MATH
- C.-Y. Zhang, “Ergodicity and its applications. II. Averaging method of some dynamical systems,” Acta Analysis Functionalis Applicata, vol. 1, no. 2, pp. 146–159, 1999. View at Zentralblatt MATH
- C. Zhang, “Ergodicity and its applications in regularity and solutions of pseudo-almost periodic equations,” Nonlinear Analysis A, vol. 46, no. 4, pp. 511–523, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. Zhang and H. Yao, “Converse problems of Fourier expansion and their applications,” Nonlinear Analysis A, vol. 56, no. 5, pp. 761–779, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Bourgain, “Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations,” Geometric and Functional Analysis, vol. 6, no. 2, pp. 201–230, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. Corduneanu, Almost Periodic Functions, Interscience Publishers, Chelsea, NY, USA, 1st edition, 1968.
- C. Corduneanu, Almost Periodic Functions, Interscience Publishers, Chelsea, NY, USA, 2nd edition, 1989.
- A. M. Fink, Almost Periodic Differential Equations, vol. 377 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1974.
- B. M. Levitan and V. V. Zhikov, Almost Periodic Functions and Differential Equations, Cambridge University Press, Cambridge, UK, 1982.
- W. Shen, “Traveling waves in time almost periodic structures governed by bistable nonlinearties, I stability and uniqueness; II. existence,” Journal of Differential Equations, vol. 159, no. 1, pp. 1–110, 1999. View at Publisher · View at Google Scholar
- F. Yang and C. Zhang, “Slowly oscillating solutions of parabolic inverse problems,” Journal of Mathematical Analysis and Applications, vol. 335, no. 2, pp. 1238–1258, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- F. Yang and C. Zhang, “Slowly oscillating solutions of a parabolic inverse problem: boundary value problems,” Boundary Value Problems, vol. 2010, Article ID 471491, 12 pages, 2010. View at Zentralblatt MATH
- C. Zhang and F. Yang, “Remotely almost periodic solutions of parabolic inverse problems,” Nonlinear Analysis A, vol. 65, no. 8, pp. 1613–1623, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- C. Zhang and F. Yang, “Pseudo almost periodic solutions to parabolic boundary value inverse problems,” Science in China A, vol. 51, no. 7, pp. 1203–1214, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, USA, 1964.
- J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993.
- B. Guo, Inverse Problem of Parabolic Partial Dfferential Equations, Science and Technology Press, Harbin, China, 1988.
- H. W. Engl, M. Hanke, and A. Neubauer, Rugularrization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.