Skip to main content
SpringerLink
Log in

Pseudo almost periodic solutions to parabolic boundary value inverse problems

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

We first define the pseudo almost periodic functions in a more general setting. Then we show the existence, uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of boundary value problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhang C. Pseudo almost periodic solutions of some differential equations. J Math Anal Appl, 181: 62–76 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Zhang C. Integration of vector-valued pseudo almost periodic functions. Proc Amer Math Soc, 121: 167–174 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dads E A, Ezzibi K. Existence of positive pseudo almost periodic solutions for some nonlinear delay integral equation arising in epidemic problems. Nonlinear Anal, 41: 1–13 (2000)

    Article  MathSciNet  Google Scholar 

  4. Dads E A, Ezzibi K, Arino O. Pseudo almost periodic solutions for some differential equations in a Banach space. Nonlinear Anal, 28: 1141–1155 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Alonso A I, Hong H, Obaya R. Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences. Appl Math Lett, 13: 131–137 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Alonso A I, Hong H, Rojo J. A class of ergodic solutions of differential equations with piecewise constant arguments. Dynam Systems Appl, 7: 561–574 (1998)

    MATH  MathSciNet  Google Scholar 

  7. Basit B, Zhang C. New almost periodic type functions and solutions of differential equations. Canad J Math, 48: 1138–1153 (1996)

    MATH  MathSciNet  Google Scholar 

  8. Cuevas C, Pinto M. Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non dense domain. Nonlinear Anal, 45: 73–83 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fan M, Ye D. Convergence dynamics and pseudo almost periodicity of a class of nonautonomous RFDEs with applications. J Math Anal Appl, 309: 598–625 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hong J, Nú:nez C. The almost periodic type difference equations. Math Comput Modelling, 28: 21–31 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  11. Hong J, Obaya R. Ergodic type solutions of some differential equations. In: Differential Equations and Nonlinear Mechanics. Dordrecht: Kluwer Academic Publishers, 2001, 135–152

    Google Scholar 

  12. Hong J, Obaya R, Gil A S. Exponential trichotomy and a class of ergodic solutions of differential equations with ergodic perturbations. Appl Math Lett, 12: 7–13 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hong J, Obaya R, Sanz A. Almost periodic type solutions of some differential equations with piecewise constant argument. Nonlinear Anal, 45: 661–688 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. Li H, Huang F, Li J. Composition of pseudo almost periodic functions and semilinear differential equation. J Math Anal Appl, 255: 436–446 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Piao D. Pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument [t+1/2]. Sci China Ser A-Math, 47: 31–38 (2004)

    Article  MathSciNet  Google Scholar 

  16. Yuan R. Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument. Nonlinear Anal, 41: 871–890 (2000)

    Article  MathSciNet  Google Scholar 

  17. Zhang C. Almost Periodic Type Functions and Ergodicity. Beijing/New York-Dordrecht-Boston-London: Science Press/Kluwer, 2003

    MATH  Google Scholar 

  18. Zhang C. Ergodicity and its applications in regularity and solutions of pseudo almost periodic equations. Nonlinear Anal, 46: 511–523 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  19. Zhang C, Yao H. Converse problems of Fourier expansion and their applications. Nonlinear Anal, 56: 761–779 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  20. Ding H S, Liang J, Guérékata G M N’, et al. Pseudo-almost periodicity of some nonautonomous evolution equations with delay. Nonlinear Anal, 67: 1412–1418 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  21. Ding H S, Liang J, Guérékata G M N’, et al. Mild pseudo-almost periodic solutions of nonautonomous semiliear evolution equations. Math Comput Modelling, 45: 579–584 (2007)

    Article  MathSciNet  Google Scholar 

  22. Bourgain J. Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations. Geom Funct Anal, 6: 201–230 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  23. Corduneanu C. Almost Periodic Functions. 2nd ed. New York: Chelsea, 1989

    MATH  Google Scholar 

  24. Fink A. Almost periodic differential equations. In: Lecture Notes in Mathematics, Vol. 377. Berlin-Heidelber-New York: Springer-Verlag, 1974

    MATH  Google Scholar 

  25. Friedman A. Partial Differential Equations of Parabolic Type. Englewood Cliffs, NJ: Prentice Hall, 1964

    MATH  Google Scholar 

  26. Levitan B M, Zhikov V V. Almost Periodic Functions and Differential Equations. Cambridge: Cambridge University Press, 1982

    MATH  Google Scholar 

  27. Liang J, Maniar L, Guérékata G M N’, et al. Existence and uniqueness of C n-almost periodic solutions to some ordinary differential equations. Nonlinear Anal, 66: 1899–1910 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  28. Shen W. Travelling waves in time almost periodic structures governed by bistable nonlinearities, I stability and uniqueness; II existence. J Differential Equations, 159: 1–101 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  29. Xiao T J, Liang J. The Cauchy problem for higher order abstract differential equations. In: Lecture Notes in Mathematics, Vol. 1701. Berlin-Heidelber-New York: Springer-Verlag, 1998, 229–249

    MATH  Google Scholar 

  30. Xiao T J, Liang J. Complete second order linear differential equations with almost periodic solutions. J Math Anal Appl, 163: 136–146 (1992)

    Article  MathSciNet  Google Scholar 

  31. Xiao T J, Liang J. Second order linear differential equations with almost periodic solutions. Acta Math Sin (New Ser), 7: 354–359 (1991)

    MATH  MathSciNet  Google Scholar 

  32. Zhang C, Yang F. Remotely almost periodic solutions of parabolic inverse problems. Nonlinear Anal, 65: 1613–1623 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  33. Zaidman S. Almost Periodic Functions in Abstract Spaces. Boston: Pitman, 1985

    MATH  Google Scholar 

  34. Guo B. Inverse Problem of Parabolic Partial Differential Equations (in Chinese). Harbin: Science and Technology Press of Heilongjiang Province, 1988

    Google Scholar 

  35. Zauderer E. Partial Differetial Equation of Applied Mathematics. New York: John Wiley & Sons, Inc., 1983

    Google Scholar 

  36. Hale J K, Sjoerd M, Verduyn L. Introduction to functional differential equations. In: Applied Mathematical Sciences, Vol. 99. New York: Springer-Verlag, 1993

    Google Scholar 

  37. Ladyzenskaja O A, Solonnikv V A, Uralceva N N. Linear and Quasi-linear Equations of Parabolic Type. Providence, Rhode Island: American Mathematical Society, 1968

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    ChuanYi Zhang & FengLin Yang

Authors
  1. ChuanYi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. FengLin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ChuanYi Zhang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10671046)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, C., Yang, F. Pseudo almost periodic solutions to parabolic boundary value inverse problems. Sci. China Ser. A-Math. 51, 1203–1214 (2008). https://doi.org/10.1007/s11425-008-0006-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-008-0006-2

Keywords

MSC(2000)

Search

Navigation