Periodic parabolic problem with discontinuous coefficients: Mathematical analysis and numerical simulation

• Alaa, Nour Eddine ^[1] ; Charkaoui, Abderrahim ^[2] ; Elaassri, Abdelwahab ^[3]
  1. [1] Université Cadi Ayyad
  2. [2] Laboratory LAMAI, Faculty of Sciences and Technics of Marrakech, University Cadi Ayyad B.P. 549, Abdelkarim Elkhattabi avenue, Marrakech - 40000
  3. [3] Laboratory MASI, Multidisiplinary Faculty of Nador, University Mohammed first

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 6, 2022, págs. 1251-1271
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5017
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• Resumen

  • This work presents a new approach for the mathematical analysis and numerical simulation of a class of periodic parabolic equations with dis- continuous coefficients. Our technique is based on the minimization of a least-squares cost function. By the means of variational calculus, we prove that the considered optimization problem admits an optimal solution. Using the Lagrangian method, we compute the gradient of the cost function associated with our problem. Finally, we give several numerical simulations that show the efficiency and robustness of our method.

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