Determination of a solely time-dependent source in a semilinear parabolic problem by means of boundary measurements

• M. 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. 433-440
• Idioma: inglés
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• Resumen

  • A semilinear parabolic problem of second order with an unknown solely time-dependent source term is studied. The missing source is recovered from an additional integral measurement over the boundary. The global in time existence, uniqueness as well as the regularity of a solution are addressed. A new numerical scheme based on Rothe’s method is designed and convergence of iterates towards the exact solution is shown.