Mathematics, Analysis, Applied Mathematics, Modeling and Simulation
3
Scopus Publications
9
Scholar Citations
2
Scholar h-index
Scopus Publications
Homogenization of the heat equation in a noncylindrical domain with randomly oscillating boundary Akambadath Keerthiyil Nandakumaran, Kasinathan Sankar Mathematical Methods in the Applied Sciences, 2022 In this article, we study the homogenization of heat equations in a domain with randomly oscillating boundary parts. The random oscillating boundary is time‐dependent and confined by a stationary random field. Here, we follow a new homogenization technique that deals with the evolving domains, which covers many applications. We obtain the asymptotic limit asε → 0 in the reference configuration, in which the heat equation becomes a parabolic equation with random oscillating coefficients in the reference domain. To the best of our knowledge, this is the first result of the homogenization of problems on the random evolving boundary domain. One of the major contributions is the corrector result which we establish in this article.
HOMOGENIZATION OF THE STOKES SYSTEM IN A DOMAIN WITH AN OSCILLATING BOUNDARY T. Muthukumar, K. Sankar Multiscale Modeling and Simulation, 2022 This article examines the homogenization issue for the Stokes system in a domain with an oscillating boundary portion. On the oscillating boundary, we impose inhomogeneous oscillating Dirichlet boundary data. The proposed method is an attempt to develop the homogenization technique for the nonstationary Stokes system on noncylindrical domains. To resolve the uniform bound of solutions with respect to heterogeneous parameters, we transform the system into a reference domain and demonstrate its existence and uniqueness in the reference domain. In order to homogenize the velocity and pressure in the reference domain, two-scale convergence is employed. In contrast to all other available homogenization techniques, the one presented in this work is easily adaptable to evolving domains. We also establish error estimates for the homogenized system approximation by transforming the system into its initial configuration.
A p-Laplacian heat equation in a non-cylindrical domain with an oscillating boundary: A homogenization process AK Nandakumaran, S Kasinathan Nonlinear Analysis: Real World Applications 88, 104501 , 2026 2026
Homogenization of the Stokes System in a Domain with an Oscillating Boundary T Muthukumar, K Sankar Multiscale Modeling & Simulation 20 (4), 1361-1393 , 2022 2022 Citations: 2
Homogenization of the heat equation in a noncylindrical domain with randomly oscillating boundary AK Nandakumaran, K Sankar Mathematical Methods in the Applied Sciences 45 (10), 6435 - 6458 , 2022 2022
Homogenization of parabolic equation in an evolving domain with an oscillating boundary T Muthukumar, JP Raymond, K Sankar Journal of Mathematical Analysis and Applications 463 (2), 838-868 , 2018 2018 Citations: 7
MOST CITED SCHOLAR PUBLICATIONS
Homogenization of parabolic equation in an evolving domain with an oscillating boundary T Muthukumar, JP Raymond, K Sankar Journal of Mathematical Analysis and Applications 463 (2), 838-868 , 2018 2018 Citations: 7
Homogenization of the Stokes System in a Domain with an Oscillating Boundary T Muthukumar, K Sankar Multiscale Modeling & Simulation 20 (4), 1361-1393 , 2022 2022 Citations: 2
A p-Laplacian heat equation in a non-cylindrical domain with an oscillating boundary: A homogenization process AK Nandakumaran, S Kasinathan Nonlinear Analysis: Real World Applications 88, 104501 , 2026 2026
Homogenization of the heat equation in a noncylindrical domain with randomly oscillating boundary AK Nandakumaran, K Sankar Mathematical Methods in the Applied Sciences 45 (10), 6435 - 6458 , 2022 2022
