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Time Asymptotically Almost Periodic Viscosity Solutions of Hamilton-Jacobi Equations

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Information Computing and Applications (ICICA 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 243))

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Abstract

To investigate the uniqueness and existence of viscosity solutions of Hamilton-Jacobi equations in the time asymptotically almost periodic case, this paper use the comparison theorem of Hamilton-Jacobi equations and the property of the asymptotically almost periodic functions to get such results.

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References

  1. Bostan, M., Namah, G.: Time periodic viscosity solutions of Hamilton-Jacobi equaitons. Commun. Pure Appl. Anal. 6(2), 389–410 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Crandall, M.G., Lions, P.-L.: Condition d’unicité pour les solutions génćralisées des équations de Hamilton-Jacobi du premier order. C. R. Acad. Sci. Paris, Sér. I Math. 292, 183–186 (1981)

    MathSciNet  MATH  Google Scholar 

  3. Crandall, M.G., Lions, P.-L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277, 1–42 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  4. Crandall, M.G., Evans, L.C., Lions, P.-L.: Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 282, 487–502 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  5. Feng, J., Katsoulakis, M.: A Comparison Principle for Hamilton-Jacobi Equations Related to Controlled Gradient Flows in Infinite Dimensions. Arch. Rational Mech. Anal. 192, 275–310 (2009), doi:10.1007/s00205-008-0133-5

    Article  MathSciNet  MATH  Google Scholar 

  6. Strömberg, T.: A counterexample to uniqueness of generalized characteristics in Hamilton-Jacobi theory. Nonlinear Analysis 74, 2758–2762 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Azagra, D., Ferrera, J., López-Mesas, F.: A maximum principle for evolution Hamilton-Jacobi equations on Riemannian manifolds. J. Math. Anal. Appl. 323, 473–480 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ibrahim, H.: Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities. Ann. I. H. Poincaré-AN 26, 415–435 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang, S., Piao, D.: Almost periodic viscosity solutions of nonlinear parabolic equations. Boundary Value Problems 2009, Article ID 873526, 15 pages (2009), doi:10.1155/2009/873526

    Google Scholar 

  10. Zhang, S., Piao, D.: Time remotely almost-periodic viscosity solutions of Hamilton-Jacobi equations. ISRN Mathematical Analysis 2011, Article ID 415358, 13 pages (2011), doi:10.5402/2011/415358

    Google Scholar 

  11. Fréchet, M.: Les fonctions asymptotiquement presque-périodiques. Revue Sci (Rev. Rose Illus.) 79, 341–354 (1941)

    MathSciNet  MATH  Google Scholar 

  12. Fréchet, M.: Les fonctions asymptotiquement presque-périodiques continues. C. R. Acad. Sci. Paris 213, 520–522 (1941)

    MathSciNet  MATH  Google Scholar 

  13. Zhang, C.: Ergodicity and asymptotically almost periodic solutions of some differential equations. International Journal of Mathematics and Mathematical Sciences 25(12), 787–800 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Buse, C.: A spectral mapping theorem for evolution semigroups on asymptotically almost periodic functions defined on the half line. Electronic Journal of Differential Equations 2002(70), 111 (2002)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Shilin Zhang

Authors
  1. Shilin Zhang
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Editor information

Editors and Affiliations

  1. College of Sciences, Hebei United University, 063000, Tangshan, Hebei, China

    Chunfeng Liu , Jincai Chang  & Aimin Yang ,  & 

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Zhang, S. (2011). Time Asymptotically Almost Periodic Viscosity Solutions of Hamilton-Jacobi Equations. In: Liu, C., Chang, J., Yang, A. (eds) Information Computing and Applications. ICICA 2011. Communications in Computer and Information Science, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27503-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-27503-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27502-9

  • Online ISBN: 978-3-642-27503-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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