Solvability of a dirichlet problem for a time fractional diffusion-wave equation in lipschitz domains

Fractional Calculus and Applied Analysis

Volumn 15, Issue 2, 2012, Pages 195-206

  Kemppainen, Jukka ^a  

^a Faculty of Technology   (Finland)

Author keywords

Boundary integral solution; Single layer potential; Time fractional diffusion wave equation

Indexed keywords

EID: 84869200108     PISSN: 13110454     EISSN: 13142444     Source Type: Journal    
DOI: 10.2478/s13540-012-0014-3     Document Type: Article

References (16)

1. A. Bamberger, T. Ha Duong, Formulation Variationelle Espace-Temps pour le Calcul par Potentiel Retard́e de la Diffraction d'une Onde Acoustique (I). Math. Meth. Appl. Sci. 8 (1986), 405-435.
2. E. Bazhlekova, Fractional Evolution Equations in Banach Spaces. PhD Thesis, Tehn. University Eindhoven (2001).
3. M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results. SIAM J. Math. Anal. 19 (1988), 613-626.
4. M. Costabel, Time-dependent problems with the boundary integral equation method. In: Encyclopedia of Computational Mechanics, Volume 1: Fundamentals, Wiley (2004).
5. A. Hanyga, Multidimensional solutions of time-fractional diffusionwave equations. Proc. R. Soc. Lond. A 458 (2002), 933-957.
6. J. Kemppainen, K. Ruotsalainen, Boundary integral solution of the time-fractional diffusion equation. Integr. Equ. Oper. Theory 64 (2009), 239-249.
7. J. Kemppainen, Behaviour of the Boundary Potentials and Boundary Integral Solution of the Time Fractional Diffusion Equation. PhD Thesis, Acta Univ. Oul. A. 548 (2010).
8. J. Kemppainen, Properties of the single layer potential for the time fractional diffusion equation. Journal of Integral Equations and Applications 23, No 3 (2011), 437-456.
9. J. Kemppainen, Boundary behaviour of the layer potentials for the time fractional diffusion equation in Lipschitz domains. Journal of Integral Equations and Applications 23, No 4 (2011), 541-564.
10. J. Kemppainen, Existence and uniqueness of the solution for a timefractional diffusion equation. Fract. Calc. Appl. Anal. 14, No 3 (2011), 411-417; DOI:10.2478/s13540-011-0025-5; at http://www.springerlink.com/content/ 1311-0454/14/3/.
11. A.A. Kilbas, M. Saigo, H-transforms: Theory and Applications. CRC Press, LLC (2004).
12. X. Li, Y. Xu, A space-time spectral method for the time fractional diffusion equation. SIAM J. Numer. Anal. 47, No 3 (2009), 2108-2131.
13. W. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, New York (2000).
14. I. Podlubny, Fractional Differential Equations. Academic Press, San Diego (1999).
15. A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev, Integrals and Series, Vol. 3. More Special Functions. Overseas Publishers Association, Amsterdam (1990).
16. W.R. Schneider, W. Wyss, Fractional diffusion and wave equations. J. Math. Phys. 30 (1989), 134-144.