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

Abstract

This work presents a new approach for the mathematical analysis and numerical simulation of a class of periodic parabolic equations with discontinuous 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.

Semilinear periodic equation with arbitrary nonlinear growth and data measure: mathematical analysis and numerical simulation

“…Hundreds of articles on periodic problems have been published in various journals and conference proceedings, although there are still more questions than answers. We refer the reader to [1][2][3][4][5][6][7][8][9][10] for a good introduction to periodic problems. These references contain review articles on ordinary periodic differential equations, which focus on the mathematical modeling of nonlinear equations and expose different solving methods.…”