Reconstruction of an unknown source parameter in a semilinear parabolic problem

• Marijke Grimmonprez ^[1] ; Marián Slodička ^[1]
  1. [1] Ghent University

     Ghent University

     Arrondissement Gent, Bélgica

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 331-345
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.12.027
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• Resumen

  • In this paper, a semilinear parabolic problem with an unknown time-dependent source function p(t) is studied. This missing parameter is reconstructed from a given measurement of the total energy/mass in the domain. The existence and uniqueness of a solution in suitable function spaces is established under minimal regularity assumptions on the data. A numerical time-discrete scheme to approximate the unique weak solution and the unknown source parameter is designed and convergence of the approximations is proved. Finally, the theoretically obtained results are supported by a numerical experiment.