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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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
Keywords
- Fuzzy partial differential equation
- Fuzzy solution
- Integral boundary condition
- Local initial condition
- Fixed point theorem