publication . Preprint . Article . Other literature type . 2015

Strong maximum principle for multi-term time-fractional diffusion equations and its application to an inverse source problem

Liu, Yikan;
Open Access English
  • Published: 23 Oct 2015
Comment: 17 pages
free text keywords: Mathematics - Analysis of PDEs, 35R11, 26A33, 35B50, 35R30, Modelling and Simulation, Computational Theory and Mathematics, Computational Mathematics
24 references, page 1 of 2

[1] Adams E E and Gelhar L W 1992 Field study of dispersion in a heterogeneous aquifer 2. Spatial moments analysis Water Resources Res. 28 3293-3307 [OpenAIRE]

[2] Al-Refai M and Luchko Y 2015 Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives Appl. Math. Comput. 257 40-51

[3] Bazhlekova E 2013 Properties of the fundamental and the impulse-response solutions of multi-term fractional differential equations, in: V. Kiryakova (Ed.), Complex Analysis and Applications '13 (Proc. Intern. Conf., Sofia, 2013), Bulg. Acad. Sci. Sofia, pp. 55-64

[4] Evans L C 2010 Partial Differential Equations 2nd ed (Providence, RI: American Mathematical Society)

[5] Gilbarg D and Trudinger N S 2001 Elliptic Partial Differential Equations of Second Order (Berlin: Springer-Verlag)

[6] Hatano Y and Hatano N 1998 Dispersive transport of ions in column experiments: an explanation of long-tailed profiles Water Resources Res. 34 1027-1033

[7] Jin B, Lazarov R, Liu Y and Zhou Z 2015 The Galerkin finite element method for a multi-term timefractional diffusion equation J. Comput. Phys. 281 825-843 [OpenAIRE]

[8] Jin B, Lazarov R and Zhou Z 2013 Error estimates for a semidiscrete finite element method for fractional order parabolic equations SIAM J. Numer. Anal. 51 445-466

[9] Jin B and Rundell W 2015 A tutorial on inverse problems for anomalous diffusion processes Inverse Problems 31 035003

[10] Li Z, Liu Y and Yamamoto M 2015 Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients Appl. Math. Comput. 257 381-397

[11] Li Z and Yamamoto M 2013 Initial-boundary value problems for linear diffusion equation with multiple time-fractional derivatives arXiv:1306.2778v2

[12] Li Z and Yamamoto M 2015 Uniqueness for inverse problems of determining orders of multi-term timefractional derivatives of diffusion equation Appl. Anal. 94 570-579

[13] Liu Y, Rundell W and Yamamoto M 2015 Strong maximum principle for fractional diffusion equations and an application to an inverse source problem (submitted) arXiv:1507.00845v1

[14] Liu F, Zhuang P, Anh V, Turner I and Burrage K 2007 Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation Appl. Math. Comput. 191 12-20

[15] Luchko Y 2009 Maximum principle for the generalized time-fractional diffusion equation J. Math. Anal. Appl. 351 218-223 [OpenAIRE]

24 references, page 1 of 2
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