Publication Cover
Applicable Analysis
An International Journal
Volume 90, 2011 - Issue 9
600
Views
52
CrossRef citations to date
0
Altmetric
Original Articles

Carleman estimate for a fractional diffusion equation with half order and application

, &
Pages 1355-1371 | Received 30 May 2010, Accepted 05 Jul 2010, Published online: 19 Jul 2011

References

  • Adams , EE and Gelhar , LW . 1992 . Field study of dispersion in a heterogeneous aquifer 2. Spatial moments analysis . Water Resources Res. , 28 : 3293 – 3307 .
  • Metzler , R and Klafter , J . 2000 . The random walk's guide to anomalous diffusion: A fractional dynamics approach . Phys. Rep. , 339 : 1 – 77 .
  • Sokolov , IM , Klafter , J and Blumen , A . 2000 . Fractional kinetics . Phys. Today , 55 : 48 – 54 .
  • Kilbas , AA , Srivastava , HM and Trujillo , JJ . 2006 . Theory and Applications of Fractional Differential Equations , Amsterdam : Elsevier .
  • Podlubny , I . 1999 . Fractional Differential Equations , San Diego : Academic Press .
  • Bazhlekova , E . 1998 . The abstract Cauchy problem for the fractional evolution equation . Fract. Calc. Appl. Anal. , 1 : 255 – 270 .
  • Luchko , Y . 2010 . Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation . Comput. Math. Appl. , 59 : 1766 – 1772 .
  • Sakamoto , K . Inverse source problems for diffusion equations and fractional diffusion equations, Ph.D. thesis, Graduate School of Mathematical Sciences, The University of Tokyo, 2009
  • Sakamoto , K. and Yamamoto , M. 2011 . Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems . J. Math. Anal. Appl. , 382 : 426 – 447 .
  • Hörmander , L . 1963 . Linear Partial Differential Operators , Berlin : Springer-Verlag .
  • Isakov , V . 2006 . Inverse Problems for Partial Differential Equations , Berlin : Springer-Verlag .
  • Carleman , T . 1939 . Sur un problème d'unicité pour les systèmes d'équations aux derivèes partielles à deux variables independentes . Ark. Mat. Astr. Fys. , 2 B : 1 – 9 .
  • Klibanov , MV and Timonov , AA . 2004 . Carleman Estimates for Coefficient Inverse Problems and Numerical Applications , Utrecht : VSP .
  • Samko , SG , Kilbas , AA and Marichev , OI . 1993 . Fractional Integrals and Derivatives , Philadelphia : Gordon and Breach Science .
  • Miller , KS and Ross , B . 1993 . An Introduction to the Fractional Calculus and Fractional Differential Equations , New York : Wiley .
  • Yamamoto , M . 2009 . Carleman estimates for parabolic equations and applications . Inverse Probl. , 25 : 123013, 75pp

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.