## Areas of Interest

- Stochastic (Partial) Differential Equations, Solvability, Large Deviation Theory, Ergodicity, Stochastic Stability, Partial Differential Equations , Solvability and Stability of Parabolic and Hyperbolic Systems, Control Theory , Deterministic and Stochastic Control Theory in Infinite Dimensions, Optimal Control Theory, Mathematical Fluid Dynamics , Stochastic Analysis and Control of Incompressible and Compressible Fluids, Optimization, Problems with Orthogonal Matrix Constraints

## Professional Background

From | Period | Position | Organisation |
---|---|---|---|

2018-07-23 | Ongoing | Assistant Professor | Indian Institute of Technology Roorkee-IIT Roorkee, INDIA |

2018-05-01 | 2 months 21 days | INSPIRE Faculty | Indian Institute of Technology Roorkee-IIT Roorkee, INDIA |

2017-08-01 | 5 months 30 days | Visiting Scientist | Indian Statistical Institute (ISI), Bangalore, INDIA |

2015-06-02 | 1 year 11 months 30 days | National Research Council (NRC) Postdoctoral Fellow | Air Force Institute of Technology (AFIT), USA |

2015-01-01 | 4 months 30 days | NBHM Postdoctoral Fellow | Indian Institute of Science Education and Research, Thiruvananthapuram (IISER-TVM), INDIA |

2009-06-01 | 1 month 30 days | FIP Substitute Lecturer | University College, Thiruvananthapuram, INDIA |

2008-10-28 | 2 months 17 days | Guest Lecturer | Mahatma Gandhi College (MG College), Thiruvananthapuram, INDIA |

## Honors and Awards

Award | Institute | Year |
---|---|---|

INSPIRE (Innovation in Science Pursuit for Inspired Research) Faculty Award | Department of Science and Technology (DST), INDIA | 2017 |

Visiting Scientist Fellowship | Indian Statistical Institute (ISI), Bangalore, INDIA | 2017 |

National Research Council (NRC) Postdoctoral Fellowship under Research Associate Programs (RAP) | National Academy of Sciences of United States of America, USA | 2015 |

NBHM Postdoctoral Fellowship | National Board of Higher Mathematics(NBHM), INDIA | 2015 |

Shyama Prasad Mukherjee (SPM) Fellowship | Council of Scientific and Industrial Research(CSIR), INDIA | 2014 |

CSIR Junior Research Fellowship (JRF) | Council of Scientific and Industrial Research(CSIR), INDIA | 2008 |

Sir T. Madhava Rao Gold Medal for securing first rank in BSc Mathematics | Kerala University, INDIA | 2006 |

## Educational Details

Degree | Subject | University | Year |
---|---|---|---|

PhD | Mathematics | Indian Institute of Science Education and Research Thiruvananthapuram (IISER-TVM), INDIA | 2014 |

MSc | Mathematics | Mar Ivanios College, Kerala University, INDIA | 2008 |

BSc | Mathematics | Mar Ivanios College, Kerala University, INDIA | 2006 |

## Memberships

- Indian Society of Industrial and Applied Mathematics (ISIAM), INDIA, Life time member

## Teaching Engagements

Title | Course Code | Class Name | Semester |
---|---|---|---|

Theory of Ordinary Differential Equations | MAN501/511 | Integrated MSc Applied Mathematics/MSc Mathematics | Autumn |

Stochastic Partial Differential Equations | MAN 914 | Pre-PhD | Autumn |

Sobolev Spaces and its Applications | MAN 913 | Pre-PhD | Spring |

Integral Equations and Calculus of Variations | MAN 533 | First year MSc Mathematics | Spring |

Probability and Statistics | MAN 006 | BTech First Year | Spring |

Ordinary and Partial Differential Equations | MAN 205 | Integrated MSc Applied Mathematics | Autumn |

Mathematics I | MAN 001 | BTech First Year | Autumn |

## Research Scholar Groups

Scholar Name | Interest |
---|---|

Kush Kinra | Control and Stochastic Analysis of Fluid Dynamic Models |

Ankit Kumar | Control and Stochastic Analysis of Fluid Dynamic Models |

Pardeep Kumar | Inverse Problems and its Applications to Partial Differential Equations |

Sumit Arora | Control Theory |

## PHDs Supervised

Topic | Scholar Name | Status of PHD | Registration Date |
---|---|---|---|

Control and Stochastic Analysis of Fluid Dynamic Models | Kush Kinra | O | 2018-01 |

Control and Stochastic Analysis of Fluid Dynamic Models | Ankit Kumar | O | 2019-01 |

Inverse Problems and its Applications to Partial Differential Equations | Pardeep Kumar | O | 2019-01 |

Control Theory (co-supervisor) | Sumit Arora | O | 2018-01 |

## Visits to outside institutions

Institute Visited | Purpose of Visit | Date |
---|---|---|

Indian Statistical Institute, Bangalore | Research | 2019-01-01 |

Wright State University, Dayton, USA | Research | 2017-01-01 |

Indian Institute of Space Sciences and Technology (IIST), INDIA | Research | 2017-01-01 |

Bergische Universitat Wuppertal, Germany | Research | 2014-01-01 |

## Invitations

Topic | Organistaion | Date |
---|---|---|

Stochastic Quasilinear Evolution Equations in UMD Banach Spaces | Spring Western American Mathematical Society Meeting, Washington State University, WA, USA | 2017-01 |

Some Recent Progress in Quasilinear Hyperbolic Systems: New Local Solvability Methods and Stochastic Analysis | 1st Northeastern Analysis Meeting (NEAM-2016), The College at Brockport, Brockport, New York, USA | 2016-01 |

Stochastic Non-Resistive Magnetohydrodynamic System with Levy Noise | Workshop on Stochastic PDEs, Department of Mathematics, University of Pittsburgh, PA, USA | 2015-01 |

## Special Lectures Delivered

Title | Place | Date |
---|---|---|

Lecture Series on Stochastic Differential Equations | Department of Mathematics, Bharatiar University, INDIA | 2017-01 |

Lecture Series on Large Deviations | Department of Mathematics and Natural Sciences, Bergische Universitat Wuppertal, Germany | 2014-01 |

## Refereed Journal Papers

40. S. Doboszczak, **M. T. Mohan** and S. S. Sritharan, Pontryagin maximum principle for the optimal control of linearized compressible Navier-Stokes equations with state constraints, Accepted in *Evolution Equations and Control Theory*, 2020.

39. S. Arora, **M. T. Mohan** and J. Dabas, Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces, Accepted in *Mathematical Control and Related Fields*, 2020.

38. T. Biswas, S. Dharmatti, P. L. N. Mahendranath and **M. T. Mohan**, On the stationary non-local Cahn-Hilliard-Navier-Stokes system: Existence, uniqueness and exponential stability, Accepted in *Asymptotic Analysis*, 2020.

37. **M. T. Mohan**, Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with "fading memory", Accepted in *Evolution Equations and Control Theory*, 2020.

36. S. Singh, S. Arora, **M. T. Mohan** and J. Dabas, Approximate controllability of second order impulsive systems with state-dependent delay in Banach spaces, Accepted in *Evolution Equations and Control Theory*, 2020.

35. **M. T. Mohan**, First order necessary conditions of optimality for the two dimensional Tidal dynamics system, Accepted in *Mathematical Control and Related Fields*, 2020.

34. T. Biswas, S. Dharmatti and M. T. Mohan, Second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn-Hilliard-Navier-Stokes equations, Accepted in Nonlinear Studies, 2020.

33. K. Ravikumar, **M. T. Mohan** and A. Anguraj, Approximate controllability of a non-autonomous evolution equation in Banach spaces, Published online in *Numerical Algebra, Control and Optimization*, 2020.

32. M. T. Mohan and A. Khan, On the generalized Burgers-Huxley equation: Existence, uniqueness, regularity, global attractors and numerical studies, Published online in Discrete and Continuous Dynamical Systems-Series B, 2020.

31. M. T. Mohan, A central limit theorem and moderate deviation principle for the stochastic 2D Oldroyd model of order one, Accepted in Stochastics and Partial Differential Equations: Analysis and Computations, 2020.

30. A. Haseena, M. Suvinthra, M. T. Mohan and K. Balachandran, Moderate deviations for stochastic Tidal dynamics equations with multiplicative Gaussian noise, Published online in Applicable Analysis, 2020.

29. M. T. Mohan, Dynamic programming and feedback analysis of the two dimensional Tidal dynamics system, Accepted in ESAIM: Control, Optimisation and Calculus of Variations, 2020.

28. S. Arora, S. Singh, J. Dabas and M. T. Mohan, Approximate controllability of semilinear impulsive functional differential systems with nonlocal conditions, Published online in IMA Journal of Mathematical Control and Information, 2020.

27. T. Biswas, S. Dharmatti and M. T. Mohan, Pontryagin’s Maximum Principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn-Hilliard-Navier-Stokes equations, Analysis, International mathematical journal of analysis and its applications, 40(3), 127–150, 2020.

26. T. Biswas, S. Dharmatti and M. T. Mohan, Maximum principle for some optimal control problems governed by 2D nonlocal Cahn-Hillard-Navier-Stokes equations, Journal of Mathematical Fluid Mechanics, **22**, Article No. 34, 1-42, 2020.

25. M. T. Mohan, Well posedness, large deviations and ergodicity of the stochastic 2D Oldroyd model of order one, Stochastic Processes and their Applications, **130**(8), 4513--4562, 2020.

24. M. T. Mohan, Global and exponential attractors for the 3D Kelvin-Voigt-Brinkman-Forchheimer equations, Discrete and Continuous Dynamical Systems-Series B, **25**(9), 3393-3436, 2020.

23. **M. T. Mohan**, On the two dimensional tidal dynamics system: stationary solution and stability, *Applicable Analysis*, **99**(10), 1795-1826, 2020.

22. **M. T. Mohan**, An extension of the Beale-Kato-Majda criterion for the 3D NavierStokes equation with hereditary viscosity, *Pure and Applied Functional Analysis,* 5(2), 407-425, 2020. Invited article in the special Issue on Partial Differential Equations and Applications in memory of Professor Aizik Volpert.

21. **M. T. Mohan**, On the three dimensional Kelvin-Voigt fluids: global solvability, exponential stability and exact controllability of Galerkin approximations, *Evolution Equations and Control Theory*, 9(2), 301-339, 2020.

20. **M. T. Mohan**, Deterministic and stochastic equations of motion arising in Oldroyd fluids of order one: Existence, uniqueness, exponential stability and invariant measures, *Stochastic Analysis and Applications*, 38(1), 1-61, 2020.

19. K. Yamazaki and **M. T. Mohan**, Well-posedness of Hall-magnetohydrodynamics System forced by Levy noise, *Stochastics and Partial Differential Equations: Analysis and Computations*, 7(3), 331-378, 2019.

18. **M. T. Mohan** and S. S. Sritharan, Stochastic Navier-Stokes equation perturbed by Levy noise with hereditary viscosity, Infinite Dimensional Analysis, Quantum Probability and Related Topics, **22**(1), 1950006 (32 pages), 2019.

17. K. T. Arasu and M. T. Mohan, Entropy of orthogonal matrices and minimum distance orthostochastic matrices from the uniform van der Waerden matrices, Discrete Optimization, **31**(1), 115-144, 2019.

16. M. T. Mohan, K. Sakthivel and S. S. Sritharan, Ergodicity for the 3D stochastic Navier-Stokes equations perturbed by Levy Noise, Mathematische Nachrichten, **292**(5), 1056–1088, 2019.

15. M. T. Mohan, On some p-almost Hadamard matrices, Operators and Matrices, **13**(1), 253-281, 2019.

14. **M. T. Mohan**, Global strong solutions of the stochastic three dimensional inviscid simplified Bardina turbulence model, *Communications on Stochastic Analysis (COSA)*, **12**(3), 249-270, 2018.

13. K. T. Arasu and M. T. Mohan, Optimization problems with orthogonal matrix constraints, Numerical Algebra, Control and Optimization (NACO), **8**(4), 413-440, 2018.

12. M. T. Mohan and S. S. Sritharan, Stochastic quasilinear symmetric hyperbolic system perturbed by Levy noise, Pure and Applied Functional Analysis, 3(1), 137-178, 2018. Invited article in special issue on Control, Optimization and PDE dedicated to Professor Viorel Barbu on the occasion of his 75th birthday.

11. S. Doboszczak, M. T. Mohan and S. S. Sritharan, Existence of optimal controls for compressible viscous flow, Journal of Mathematical Fluid Mechanics, 20(1), 199-211, 2018.

10. U. Manna, M. T. Mohan and S. S. Sritharan, Stochastic non-resistive magnetohydrodynamic system with Levy noise, Random Operators and Stochastic Equations, 25(3), 155-194, 2017.

9. M. T. Mohan and S. S. Sritharan, Lp−solutions of stochastic Navier-Stokes equations subject to Levy noise with Lm(Rm) initial data, Evolution Equations and Control Theory (EECT), 6(3), 409-425, 2017.

8. M. T. Mohan and S. S. Sritharan, Stochastic quasilinear evolution equations in UMD Banach spaces, Mathematische Nachrichten, 290(13), 1971-1990, 2017.

7. M. T. Mohan and S. S. Sritharan, Ergodic control of stochastic Navier-Stokes equation with Levy noise, Communications on Stochastic Analysis (COSA), 10(3), 389-404, 2016.

6. M. T. Mohan and S. S. Sritharan, Stochastic Euler equations of fluid dynamics with Levy noise, Asymptotic Analysis, 99(1–2), 67-103, 2016.

5. M. T. Mohan and S. S. Sritharan, New methods for local solvability of quasilinear symmetric hyperbolic system, Evolution Equations and Control Theory (EECT), 5(2), 273-302, 2016.

4. U. Manna, M. T. Mohan and S. S. Sritharan, Stochastic Navier-Stokes equations in unbounded channel domains, Journal of Mathematical Fluid Mechanics, 17, 47-86, 2015.

3. U. Manna and M. T. Mohan, Two-dimensional magnetohydrodynamic systems with jump processes: Well posedness and invariant measures, Communications on Stochastic Analysis (COSA), 7(1), 153-178, 2013.

2. U. Manna and M. T. Mohan, Large deviations for the shell model of turbulence perturbed by Levy noise, Communications on Stochastic Analysis (COSA), 7(1), 39-63, 2013.

1. U. Manna and M. T. Mohan, Shell model of turbulence perturbed by Levy noise, Nonlinear Differential Equations and Applications (NoDEA), 18, 615-648, 2011.

**Conference Proceedings: **

1. M. T. Mohan and S. S. Sritharan, Frequency truncation method for quasilinear symmetrizable hyperbolic systems, Proceeding of ICMAA-2016, Journal of Analysis, 28(1), 117-140, 2020.