Identification of a memory kernel in a semilinear integrodifferential parabolic problem with applications in heat conduction with memory

• Autores: K. Van Bockstal, R.H. De Staelen, Marián Slodicka
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 196-207
• Idioma: inglés
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• Resumen

  • In this contribution, the reconstruction of a solely time-dependent convolution kernel is studied in an inverse problem arising in the theory of heat conduction for materials with memory. The missing kernel is recovered from a measurement of the average of temperature. The existence, uniqueness and regularity of a weak solution is addressed. More specific, a new numerical algorithm based on Rothe’s method is designed. The convergence of iterates to the exact solution is shown.