Semilinear periodic parabolic problem with discontinuous coefficients: Mathematical analysis and numerical simulation

We develop a new technique to mathematically analyze and numerically simulate the weak periodic solution class of semilinear parabolic equations with discontinuous coefficients. reformulate our problem into minimization via least-squares cost function. By using variational calculus theory, we establish existence an optimal based on Lagrangian method, calculate derivative To illustrate validity efficiency proposed present some numerical examples different periods time diverse choices