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The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations

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Abstract

Fuzzy hyperbolic partial differential equation, one kind of uncertain differential equations, is a very important field of study not only in theory but also in application. This paper provides a theoretical foundation of numerical solution methods for fuzzy hyperbolic equations by considering sufficient conditions to ensure the existence and uniqueness of fuzzy solution. New weighted metrics are introduced to investigate the solvability for boundary valued problems of fuzzy hyperbolic equations and an extended result for more general classes of hyperbolic equations is initiated. Moreover, the continuity of the Zadeh’s extension principle is used in some illustrative examples with some numerical simulations for \(\alpha \)-cuts of fuzzy solutions.

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Acknowledgments

The authors would like to thank Editor-in-Chiefs, Prof. Shu-Cherng Fang; Associate Editor; anonymous reviewers; Prof. Bui Cong Cuong (VAST), Dr. Tran Dinh Ke (HNUE) for their comments and their valuable suggestions that improved the quality and clarity of the paper. This work is supported by NAFOSTED, Vietnam under contract No.102.01-2012.14.

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Authors and Affiliations

  1. Department of Basic Sciences, University of Transport and Communications, Hanoi, Vietnam

    Hoang Viet Long

  2. Department of Mathematics, Hanoi University of Education, Hanoi, Vietnam

    Nguyen Thi Kim Son

  3. Department of Mathematics, Hai Phong University, Hai Phong, Vietnam

    Nguyen Thi My Ha

  4. Centre for High Performance of Computing, VNU University of Science, Vietnam National University, Hanoi, Vietnam

    Le Hoang Son

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  1. Hoang Viet Long
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  2. Nguyen Thi Kim Son
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  3. Nguyen Thi My Ha
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Correspondence to Hoang Viet Long.

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Long, H.V., Son, N.T.K., Ha, N.T.M. et al. The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations. Fuzzy Optim Decis Making 13, 435–462 (2014). https://doi.org/10.1007/s10700-014-9186-0

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  • DOI: https://doi.org/10.1007/s10700-014-9186-0

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