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Pirzada, U. M.; Vakaskar, D. C.

Fuzzy solution of homogeneous heat equation having solution in Fourier series form. (English) Zbl 1483.35334

S\(\vec{\text{e}}\)MA J. 76, No. 1, 181-194 (2019).
Summary: While solving practical problems, we often come across situations where the system involves fuzziness. The mathematical models resulting in partial differential equations, involve fuzzy parameters and variables. In available literature, methods are presented mainly for solving non-homogeneous fuzzy partial differential equations (see [T. Allah Viranloo, Comput. Methods Appl. Math. 2, No. 3, 233–242 (2002; Zbl 1011.65077); with N. Taheri, Int. J. Contemp. Math. Sci. 4, No. 1–4, 105–114 (2009; Zbl 1181.35314); with M. A. Kermani, Iran. J. Fuzzy Syst. 7, No. 3, 33–50 (2010; Zbl 1262.65142); with S. Abbasbandy and H. Rouhparvar, “The exact solutions of fuzzy wave-like equations with variable coefficients by a variational iteration method”, Appl. Soft Comput. 11, No. 2, 2186–2192 (2011; doi:10.1016/j.asoc.2010.07.018)]). We present a method to find the solution of homogeneous fuzzy heat equations with fuzzy Dirichlet boundary conditions. We consider the fuzziness in zero in the homogeneous equation as well as in the boundary conditions. The initial conditions are also in fuzzy form. Further, we study the solution of fuzzy heat equation when the fuzzy initial conditions are represent as a Fourier series.

MSC:

35R13 Fuzzy partial differential equations
35K51 Initial-boundary value problems for second-order parabolic systems

Keywords:

fuzzy heat equation; Seikkala solution; Fourier series; fuzzy Dirichlet boundary conditions; fuzzy initial conditions

Citations:

Zbl 1011.65077; Zbl 1181.35314; Zbl 1262.65142
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Full Text: DOI

References:

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