The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations
http://repository.vnu.edu.vn/handle/VNU_123/29734
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 $$\alpha $$α-cuts of fuzzy solutions
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 $$\alpha $$α-cuts of fuzzy solutions
| Title: | The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations |
| Authors: | Long, Hoang Viet Kim, Nguyen Thi Ha, Nguyen Thi My Son, Le Hoang |
| Keywords: | Fixed point theorem Fuzzy partial differential equation Fuzzy solution Integral boundary condition Integral boundary condition |
| Issue Date: | 2014 |
| Publisher: | Fuzzy Optimization and Decision Making |
| Citation: | Scopus |
| 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 $$\alpha $$α-cuts of fuzzy solutions |
| Description: | Fuzzy Optimization and Decision Making, Volume 13, Issue 4, 1 December 2014, Pages 435-462 Fuzzy Optimization and Decision Making |
| URI: | http://repository.vnu.edu.vn/handle/VNU_123/29734 |
| ISSN: | 15684539 |
| Appears in Collections: | Bài báo của ĐHQGHN trong Scopus |
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