Dr. Ankik Kumar Giri

Research

Partial Integro-Differential Equations Coagulation-Fragmenation Models, Well-posedness, Regularity, Mass-conservation, Gelation,
Large time behaviour, Stationary solutions, Self-similar profiles, Numerical Methods, Error Analysis

Stochastic Partial Differential Equations Well-posedness, Regularity and Convergence Analysis of Numerical Methods

Inverse Problems Variational Regularization and Iterative regularization, Stability Estimates, Regularized Solutions, Convergence, Convergence Rates

Research Group

Current Ph.D. Students

Pratibha Verma Population Balance Models

Mashkhoor Ali Study of Coagulation-Fragmentation Equations using Semigroup Theory Approach

Saroj Si Analysis and numerics of Coagulation-Fragmentation Models with Growth

Ram Gopal Jaiswal Self-Similar and Stationary Solutions to the Population Balance Equations

Former Ph.D. Students

Prasanta Kumar Barik Nonsingular and Singular Coagulation Models with Linear and Nonlinear Breakage

Vivek Kumar On Well-Posedness for Generalized Stochastic Burgers-Type Equations

Pooja rai Oort-Hulst-Safronov coagulation model and its discrete counterpart with singular and nonsingluar unbounded coefficients

Gaurav Mittal Regularization for Nonlinear Inverse Problems via Stability Constraints

Publications

Convergence Analysis of iteratively regularized Gauss-Newton method with frozen derivative in Banach spaces, Accepted in J. Inverse and Ill-posed Problems (with G. Mittal)
Novel multi-level projected iteration to solve inverse problems with nearly optimal accuracy, J. Optim. Theory Appl., 2022 (with G. Mittal)
Mass-conserving weak solutions to Oort-Hulst-Safronov coagulation equation with singular rates, Journal of Differential Equations, 326, 164--200, 2022 (with P.K. Barik, P. Rai)
On a generalized stochastic Burger's equation perturbed by Volterra noise, J. Math. Anal. Appl. 506(1), Article No. 125638, 2022 (with V. Kumar, M.T. Mohan)
Convergence rates for iteratively regularized Gauss-Newton method subject to stability constraints, J. Comput. Appl. Math. 400, Article No. 113744, 2022(with G. Mittal)
Existence and non-existence for collision-induced breakage equation, SIAM J. Math. Anal. 53(4), 4605--4636, 2021 (with Ph. Laurencot)
A novel two-point gradient method for regularization of inverse problems in Banach spaces, Applicable Analysis (with G. Mittal)
Existence and uniqueness of weak solutions to the singular coagulation equation with collisional breakage, NoDEA Nonlinear Differential Equations Appl. 28, Article No. 34, 2021(with P.K. Barik)
Weak solutions to the collision-induced breakage equation with dominating coagulation, Journal of Differential Equations 288, 690-729, 2021 (with Ph. Laurencot)
Mass-conserving weak solutions to the coagulation and collisional breakage equation with singular rates, Kinetic and Related Models, 14(2):389-406, 2021 (with P.K. Barik, R. Kumar)
Iteratively regularized Landweber iteration method: Convergence analysis via Holder Stability, Applied Mathematics and Computation, 392: Article No. 125744, 2021 (with G. Mittal)
On a mixed fractional Burgers type equation with polynomial nonlinearity and perturbed by fractional Brownian sheet, Stochastic Analysis and Applications, 39(4), 610-630, 2021 (with V. Kumar)
Weak solutions to the continuous coagulation model with collisional breakage, Discrete and Continuous Dynamical Systems-Series A, 40(11), 6115-6133, 2020 (with P.K. Barik)
On Variational Regularization: Finite dimension and Holder stability, J. Inverse and Ill-posed Problems, 29(2): 283-294, 2021(with G. Mittal)
Global classical solutions to the continuous coagulation equation with collisional breakage, Z. Angew. Math. Phys. (ZAMP) 71: Article No. 38, 1-23, 2020 ( with P.K. Barik)
Mass-Conserving solutions to the Smoluchowski coagulation equations with singular kernel, Proceedings of Royal Society Edinburgh A 150(4), 18-5-1825, 2020 ( with P.K. Barik and Ph. Laurençot)
Generalized stochastic Burgers' equation with non-Lipschitz diffusion coefficient, Commun. Stoch. Anal., 12(3), 329-342, 2018 (with V. Kumar)
A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation, Kinetic and Related Models, 11 (5), 1125-1138, 2018 (with P.K. Barik)
Convergence of the cell average technique for Smoluchowski coagulation equation, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN) , 49 (2), 349-372, 2015 arxiv preprint (with A.K. Nagar)
On the uniqueness for coagulation and multiple fragmentation equation, Kinetic and Related Models (KRM), 6(3): 589-599, 2013.
Stochastic Burger's equation with polynomial nonlinearity driven by Levy process, Commun. Stoch. Anal. (COSA), 7(1): 91-112, 2013 (with E. Hausenblas)
Convergence analysis of sectional methods for solving aggregation population balance equations: The fixed pivot technique, Nonlinear Analysis: Real World Applications, 14: 2068-2090, 2013 (with E. Hausenblas)
Weak solutions to the continuous coagulation equation with multiple fragmentation, Nonlinear Analysis: Theory, Methods and Applications, 75: 2199-2208, 2012 (with Ph. Laurencot, and G. Warnecke)
Convergence of the fixed pivot technique for continuous Smoluchowski coagulation equation, Proc. Appl. Math. Mech., 11:701-702:2011 (with E. Hausenblas)
Uniqueness for coagulation-fragmentation equations with strong fragmentation, Z. Angew. Math. Phys. (ZAMP) 62: 1047-1063, 2011 (with G. Warnecke)
The continuous coagulation equation with multiple fragmentation, J. Math. Anal. Appl. 374: 71-87, 2011 (with J. Kumar and G. Warnecke)

Collaborators

Prof. Philippe Laurencot (CRNS, University of Toulouse, France)

Prof. Volker John (Weierstass Institute for Applied Analysis and Stochastics and Freie Unversity Berlin, Germany)

Prof. Otmar Scherzer (Radon Institute for Computational and Applied Mathematics (RICAM) Linz and University of Vienna, Austria)

Prof. Erika Hausenblas (University of Leoben, Austria)

Prof. Gerald Warnecke (University of Magdeburg, Germany)

Prof. Fernando da Costa (IST Lisbon and University of Aberta Lisbon, Portugal)

Prof. Michael Grinfeld (University of Strathclyde, Glasgow, UK)

Prof. Youcef Mammeri (University of Picardie Jules Verne, Amiens, France)

Prof. Joaquim Correia (University of Evora, Portugal)

Prof. Nabil Badjaoui (University of Picardie Jules Verne, Amiens, France)

Prof. Marilia Pires (University of Evora, Portugal)

Prof. Jacek Banasiak (University of Pretoria, South Africa)

Scientific Research Projects

Indo-French joint project on "Collision-induced Fragmentation and Coagulation: Dynamics and Numerics" funded by IFCAM (Indo-French Centre for Applied Mathematics), August 2019-March 2023. (with Prof. Philippe Laurencot, CNRS, University of Toulouse, France)

Indo-German joint project on "Analysis and Numerical Methods for Population Balance Equations" funded by DST-DAAD, July 2019-June 2021. (with Prof. Volker John, WIAS Berlin, germany)

"Coagulation-fragmentation models: Well-posedness, Numerical approximations and Asymptotic analysis" funded by SERB, New Delhi, India, October 2016-October 2019.

Faculty Initiation Grant (FIG) funded by IIT Roorkeel, September 2015-September 2018.