Geodesic
Semilinear periodic parabolic problem with discontinuous coefficients: mathematical analysis and numerical simulation
Filomat, Tome 37 (2023) no. 7, p. 2151

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DOI

We develop a new technique to mathematically analyze and numerically simulate the weak periodic solution to a class of semilinear periodic parabolic equations with discontinuous coefficients. We reformulate our problem into a minimization problem via a least-squares cost function. By using variational calculus theory, we establish the existence of an optimal solution and based on the Lagrangian method, we calculate the derivative of our cost function. To illustrate the validity and efficiency of our proposed method, we present some numerical examples with different periods of time and diverse choices of discontinuous coefficients.
DOI : 10.2298/FIL2307151A
Classification : 35K55, 35B10, 35K59
Keywords: Weak periodic solutions, discontinuous coefficients, optimization, Lagrangian, least-squares 
Hamza Alaa; Malika El Ghabi; Abderrahim Charkaoui. Semilinear periodic parabolic problem with discontinuous coefficients: mathematical analysis and numerical simulation. Filomat, Tome 37 (2023) no. 7, p. 2151 . doi: 10.2298/FIL2307151A
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     title = {Semilinear periodic parabolic problem with discontinuous coefficients: mathematical analysis and numerical simulation},
     journal = {Filomat},
     pages = {2151 },
     year = {2023},
     volume = {37},
     number = {7},
     doi = {10.2298/FIL2307151A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2307151A/}
}
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