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SUMMARY:Determination of an additive source in the heat equation - Lesnic\
 , D (University of Leeds)
DTSTART:20140213T110000Z
DTEND:20140213T114500Z
UID:TALK50848@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Dinh Nho Hao (Hanoi Institute of Mathematics\, Vie
 tnam)\, Areena Hazanee (University of Leeds\, UK)\, Mikola Ivanchov (Ivan 
 Franko National University of Lviv\, Ukraine)\, Phan Xuan Thanh (Hanoi Uni
 versity of Science and Technology\, Vietnam) \n\nWater contaminants arisin
 g from distributed or non-point sources deliver pollutants indirectly thro
 ugh environmental changes\, e.g. a fertilizer is carried into a river by r
 ain which in turn will affect the aquatic life. Then\, in this inverse pro
 blem of water pollution\, an unknown source in the governing equation need
 s to be determined from the measurements of the concentration or other pro
 jections of the dependent variable of the model. A similar inverse problem
 \, arises in heat transfer. \n\nInverse source problems for the heat equat
 ion\, especially in the one-dimensional transient case\, have received con
 siderable attention in recent years. In most of the previous studies\, in 
 order to ensure a unique solution\, the unknown heat source was assumed to
  depend on only one of the independent variables\, namely\, space or time\
 , or on the dependent variable\, namely\, concentration/temperature. It is
  the puropose of our analysis to investigate an extended case in which the
  unknown source is assumed to depend on both space and time\, but which is
  additively separated into two unknown coefficient source functions\, name
 ly\, one component dependent on space and another one dependent on time. T
 he additional overspecified conditions can be a couple of local or nonloca
 l measurements of the concentration/temperature in space or time. \n\nThe 
 unique solvability of this linear inverse problem in classical Holder spac
 es is proved\; however\, the problem is still ill-posed since small errors
  in the input data cause large errors in the output source. In order to ob
 tain a stable reconstruction the Tikhonov regularization or the iterative 
 conjugate gradient method is employed. Numerical results will be presented
  and discussed. \n
LOCATION:Seminar Room 1\, Newton Institute
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