Determine the special term of a two-dimensional heat source

References

• Lions , JL and Magenès , E . 1968 . Problèmes aux Limites non Homogènes et Applications, Vol. 1 , Paris : Dunod .
   Google Scholar
• Isakov , V . 1990 . Inverse Source Problems, Mathematical Surveys and Monographs Series, Vol. 34 , RI : AMS, Providence .
   Google Scholar
• Cannon , JR and Esteva , SP . 1990 . Some stability estimates for a heat source in terms of over specified data in the 3-D heat equation . J. Math. Anal. Appl , 147 : 363 – 371 .
   Google Scholar
• Cannon , JR and Esteva , SP . 1991 . Uniqueness and stability of 3D heat source . Inverse Probl. , 7 : 57 – 62 .
   Web of Science ®Google Scholar
• Yamamoto , M . 1993 . Conditional stability in determination of force terms of heat equations in a rectangle . Math. Comput. Model. , 18 : 79 – 88 .
   Web of Science ®Google Scholar
• M. Yamamoto, Conditional stability in determination of densities of heat source in a bounded domain, in Control and estimation of distributed parameter systems: Nonlinear phenomena, W. Desch, E. Kappel and K. Kunisch, eds. (Vorau, 1993), International Series of Numerical Mathematics 118 (1994), pp. 359–370. Birkhauser, Babel
   Google Scholar
• Yamamoto , M and Zou , J . 2001 . Simultaneous reconstruction of the initial temperature and heat radiative coefficient . Inverse Probl. , 17 : 1181 – 1202 .
   Web of Science ®Google Scholar
• Saitoh , S , Tuan , VK and Yamamoto , M . 2002 . Reverse convolution inequalities and applications to inverse heat source problems . JIPAM. J. Inequal. Pure Appl. Math. , 3 ( 5 ) Article 80 (electronic). Available at http://jipam.vu.edu.au/article.php?sid=232
   Google Scholar
• Saitoh , S , Tuan , VK and Yamamoto , M . 2003 . Convolution inequalities and applications . JIPAM. J. Inequal. Pure. Appl. Math. , 4 ( 3 ) Article 50 (electronic). Available at http://jipam.vu.edu.au/article.php?sid=288
   Google Scholar
• Choulli , M and Yamamoto , M . 2004 . Conditional stability in determining a heat source . J Inverse Ill-Posed Problems , 12 ( 3 ) : 233 – 243 .
   Google Scholar
• Wang , P and Zheng , K . 1999 . Determination of the source/sink term in a heat equation, Fourth Mississippi State Conference on Differential Equations and Computational Simulations . Electronic Journal of Differential Equations, Conference , 03 : 119 – 125 . Starkville, Mississippi
   Google Scholar
• Shidfar , A , Zakeri , A and Neisi , A . 2005 . A two-dimensional inverse heat conduction problem for estimating heat source . Int. J. Math. Sci , 10 : 1933 – 1941 .
   Google Scholar
• Farcas , A and Lesnic , D . 2006 . The boundary-element method for the determination of a heat source dependent on one variable . J. Engrg. Math. , 54 ( 4 ) : 375 – 388 .
   Web of Science ®Google Scholar
• Cannon , JR . 1968 . Determination of an unknown heat source from overspecified boundary data . SIAM J. Numer. Anal , 5 : 275 – 286 .
   Web of Science ®Google Scholar
• Wang , P and Zheng , K . 2006 . Reconstruction of spacial heat sources in heat conduction problems . Appl. Anal. , 85 ( 5 ) : 459 – 465 .
   Google Scholar
• Trong , DD , Long , NT and Dinh Alain , PN . 2005 . Nonhomogeneous heat equation: Identification and regularization for the inhomogeneous term . J. Math. Anal. Appl. , 312 : 93 – 104 .
   Web of Science ®Google Scholar
• Trong , DD , Quan , PH and Dinh Alain , PN . 2006 . Determination of a two-dimensional heat source: Uniqueness, regularization and error estimate . J. Comput. Appl. Math. , 191 : 50 – 67 .
   Google Scholar
• Burikin , AA and Denisov , AM . 1995 . Determination of the unknown sources in the heat condition equation . Comp. Maths. Model , 8 : 309 – 313S .
   Google Scholar
• Levin , BYa . 1996 . Lectures on Entire Functions, Translations of Mathematical Monographs, Vol. 150 , RI : AMS, Providence .
   Google Scholar