Dr. Meraj Alam currently works as an Assistant Professor at the department of mathematics at Mahindra University. He completed his Ph.D. thesis on an interesting topic “Existence and Uniqueness Results for Biphasic Mixture Models to Tumors”, Department of Mathematics, Indian Institute of Technology Kharagpur (2020). His Ph.D. thesis is focused on mathematical modeling and analysis of biphasic mixture models (nonlinear partial differential equations) that describe the coupled phenomena of fluid flow and solid phase deformation inside soft bio-materials such as tumors. He mainly works on developing the well-posedness (existence, uniqueness, and continuous dependence on data) in a weak sense to the nonlinear partial differential equations of the type parabolic, hyperbolic and elliptic systems using some well-known mathematical techniques. Namely, the semi-discrete Galerkin method, fixed-point theorems, monotone operator approach, Lax-Milgram lemma, and Babuska-Brezzi condition etc.
Articles Published in Peer-Reviewed Journals
- Timir Karmakar, Meraj Alam, G. P. Raja Sekhar, Analysis of Brinkman-Forchheimer extended Darcy’s model in a fluid saturated anisotropic porous channel (Communications on Pure & Applied Analysis (2021); (SCIE, I.F.: 1.916) (ISSN 1534-0392) DOI: http://dx.doi.org/10.3934/cpaa.2022001.
- Meraj Alam, M. Byrne, G. P. Raja Sekhar, Existence and uniqueness results on biphasic mixture model for an in-vivo tumor, Applicable Analysis, (2021), (SCIE, I.F.: 1.429) (ISSN: 1563-504X). DOI: https://doi.org/10.1080/00036811.2021.1895122
- Meraj Alam, Dey, G. P. Raja Sekhar, Mathematical modeling and analysis of hydroelastodynamics inside a solid tumor containing deformable tissue. Z Angew Math Mech. Vol: 99 (5) (2019); e201800223, (SCIE, I.F.: 1.603) (ISSN: 1521-4001). DOI: https://doi.org/10.1002/zamm.201800223
- Meraj Alam, B. Dey, G. P. Raja Sekhar, Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor, Theoretical and Applied Mechanics Vol: 45 (2) (2018); 253-278, (Scopus, ESCI, ISSN: 1450-5584). DOI: https://doi.org/10.2298/TAM180810014A
- G. P. Raja Sekhar, Meraj Alam, Fixed Point Theorems and Applications to Fluid Flow Problems, The Special Issue of The Proceedings of Telangana Academy of Sciences Vol: 01 (01), 2020, 134-146
Broad Areas of Research:
- Analysis (well-posedness in weak sense) of nonlinear partial differential equations of the types: elliptic, parabolic, and second order hyperbolic.
- Mathematical modeling of multi-phase flow through deformable porous medium
- Applied functional analysis (Applications of fixed point and monotone operator theory)