Some Nonlocal Boundary-Value Problems for the Biparabolic Evolution Equation and Its Fractional-Differential Analog
- 4 Downloads
For the biparabolic partial differential evolution equation and its fractional differential generalization, statements are made and closed-form solutions of some boundary-value problems with nonlocal boundary conditions are obtained. Variants of direct and inverse problem statements are considered. The mathematical formulation of the inverse problem involves the search, together with the solution of the original integro-differential equation of fractional order, of its unknown right-hand side as well, which functionally depends only on the geometric variable.
Keywordsbiparabolic evolution equation fractional-differential analog of biparabolic equation nonlocal boundary-value problem inverse problem biorthogonal systems of functions
Unable to display preview. Download preview PDF.
- 2.E. I. Kartashov, Analytical Methods in the Theory of Heat Conduction in Solids [in Russian], Vysshaya Shkola, Moscow (1979).Google Scholar
- 3.A. V. Lykov, Heat and Mass Exchange [in Russian], Energiya, Moscow (1978).Google Scholar
- 6.V. I. Fushchich, “Symmetry and partial solutions to some multidimensional equations of mathematical physics,” Theoretical-Algebraic Methods in Problems of Mathematical Physics [in Russian], Inst. Math. AS UkrSSR (1983), pp. 4–22.Google Scholar
- 8.V. M. Bulavatsky, “Mathematical modeling of filtrational consolidation of soil under motion of saline solutions on the basis of biparabolic model,” J. Autom. Inform. Sci., Vol. 35, No. 8, 13–22 (2003).Google Scholar
- 10.V. V. Uchaikin, The Method of Fractional Derivatives [in Russian], Artishok, Ulyanovsk (2008).Google Scholar
- 17.A. M. Nakhushev, Fractional Calculus and its Application [in Russian], Fizmatlit, Moscow (2003).Google Scholar
- 18.R. P. Meilanov, V. D. Beibalaev, and M. R. Shibanova, Applied Aspects of Fractional Calculus, Palmarium Acad. Publ., Saarbrucken (2012).Google Scholar
- 25.E. I. Moiseyev, “Solving one nonlocal boundary-value problem by the spectral method,” Diff. Uravneniya, Vol. 35, No. 8, 1094–1100 (1999).Google Scholar
- 26.V. M. Bulavatsky, Iu. G. Kryvonos, and V. V. Skopetsky, Nonclassical Mathematical Models of Heat and Mass Transfer Processes [in Ukrainian], Naukova Dumka, Kyiv (2005).Google Scholar
- 27.I. A. Kaliev and M. M. Sabitova, “Problems of determining the temperature and density of heat sources from the initial and terminal temperatures,” Sibirskii Zhurnal Industr. Matem., Vol. 12, No. 1 (37), 89–97 (2009).Google Scholar