Broadly, my field of research is partial differential equations. My research interests concern with the transport processes inside a porous medium, analysis of linear and nonlinear parabolic partial differential equations (PDEs) and homogenization theory. Several problems in the fields of physics, chemistry, biology and engineering sciences are governed by ordinary and partial differential equations, for example flow inside a porous medium. Transport processes in a porous medium (concrete carbonation, groundwater flow, leaching of saline soil, waste water treatment, e.g.) have been extensively studied by mathematician, hydrologist, geologist and others, and they intrigue my curiosity too. Below are my research areas:

1. Applied Analysis
a. Partial Differential Equations
b. Homogenization Theory (Periodic & Stochastic)
c. Variational Methods
d. Transport Processes in Heterogeneous Medium
e. Plasticity

2. Mathematical Biology
  a. PK/PD Modeling
  b. Mathematical Modelling of Renal Physiology
  c. Diabetic Nephropathy
  d. Cardiovascular Modeling
e. Micro-Pore Tissue Modeling

All Publications

Global existence and uniqueness of a system of nonlinear multi-species diffusion-reaction equations in the presence of homogeneous Neumann boundary conditions in an H^{1,p} setting by Mahato H. S., Boehm M. Journal of Applied Analysis and Computation 3 357-376 (2013)
Homogenization of a system of multi-species diffusion-reaction-dissolution-precipitation equations in the presence of inflow-outflow boundary conditions by Mahato H. S., Boehm M. , Knabner P. , Kraeutle S. Advances in Mathematical Sciences and Applications 26 39-81 (2017)
Homogenization of a system of semilinear diffusion-reaction equations in an H^{1,p} setting by Mahato H. S., Boehm M. Electronic Journal of Differential Equations 1-22 (2013)
An existence result for a system of coupled semilinear diffusion-reaction equations with flux boundary conditions by Mahato H. S., Boehm M. European Journal of Applied Mathematics 1-22 (2014)
Existence and averaging of a system of nonlinear parabolic equations with mixed Neumann-Robin interface conditions by Mahato H. S. Advances and Applications in Fluid Mechanics 19 473-488 (2016)
Strong solvability up to clogging of an effective diffusion--precipitation model in an evolving porous medium by Mahato H. S., Knabner P. , Schulz R. , Ray N. , Frank F. European Journal of Applied Mathematics 1-29 (2016)
Upscaling of Helmholtz equation originating in transmission through metallic gratings in meta-materials by Mahato H. S. The Scientific World Journal 1-14 (2016)
Homogenization of Cahn-Hilliard type equations in a perforated porous medium by Mahato H. S., Banas L. Asymptotic Analysis 105 77-95 (2017)
A note on extension type theorems in homogenization of periodic domains by Mahato H. S. N-W European Journal of Mathematics 3 107-122 (2017)
Numerical simulations for a two scale model in a porous medium by Mahato H. S. Numerical Analysis and Applications 10 - (2017)

Completed Projects

Co-Principal Investigator

Modeling, Analysis and Homogenization of Biphasic Mixture Models for Tissue Engineering Applications Anusandhan National Research Foundation (ANRF)

Alumni members

Ph. D. Students

Haradhan Dutta

Area of Research: Partial Differential Equations, Applied Analysis, Homogenization Theory

Sagun Hansda

Area of Research: Partial Differential Equations, Applied Analysis, Flow in porous media, Homogenization Theory

Swarupananda Banerjee

Area of Research: Partial Differential Equations, Applied Analysis, Poro-elastic and Poro-visco-elastic problems