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Ankik Kumar Giri
Associate Professor
ankik.giri[at]ma.iitr.ac.in
https://www.iitr.ac.in/ankikgiri/
Research Interests

Biosketch
Educational Details
Professional Background

Research
Projects
Publications
Patents
Books
Collaborations

Honours and Awards
Honors
Memberships

Teaching Engagements
Teaching Engagements

Students
Supervisions
Associate Scholars

Miscellaneous
Events
Visits
Administrative Positions
Miscellaneous
Research Interests
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, Regularization Theory for Inverse Problems: Variational Regularization and Iterative regularization, Stability Estimates, Regularized Solutions, Convergence, Convergence Rates
BioSketch
Educational Details
International Max-Planck Research School (IMPRS) at Otto-Von-Guericke Unversity, Magdeburg, Germany
2010
PhD, Mathematics
Indian Institute of Technology Roorkee, India
2005
M.Sc., Applied Mathematics
Professional Background
Visiting Researcher
05 Sep 2016 - 07 Sep 2016
Max-Planck Institute Leipzig, Germany
Visiting Researcher
01 Jul 2018 - 15 Jul 2018
CAMGSD at IST-Lisbon, Portugal
Visiting Researcher
23 Jun 2019 - 14 Jul 2019
Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany
Doctoral fellow
17 Jul 2007 - 31 May 2010
International Max-Planck Research School (IMPRS), Otto-von-Guericke-University, Magdeburg, Germany
Associate Professor
17 Dec 2019 - Present
Department of Mathematics, IIT Roorke
Assistant Professor
23 Jun 2014 - 16 Dec 2019
Department of Mathematics, IIT Roorkee, India
Research Scientist
01 May 2012 - 30 Jun 2014
Johann Radon Institute for Computational and Applied Mathematics (RICAM) Austrian Academy of Science
Post Docotoral Fellow
01 Jun 2010 - 30 Apr 2012
Chair for Applied Mathematics, Montan University Leoben, Austria
Visiting Researcher
20 Jun 2018 - 30 Jun 2018
LAMFA, CNRS, University of Picardie Jules Verne, Amiens, France
Research
Projects
TOPIC START DATE FIELD DESCRIPTION FINANCIAL OUTLAY FUNDING AGENCY OTHER OFFICERS
Collision-induced Fragmentation and Coagulation: Dynamics and Numerics 01 Aug 2019 Partial-integro differential equations NA IFCAM (Indo-French Centre for Applied Mathematics) Prof. Philippe Laurencot, CNRS, University of Toulouse, France
Analysis and Numerical Methods for Population Balance Equations 18 Jul 2019 Partial Differential Equations NA DST-DAAD (Indo-German) Prof. Volker John, WIAS Berlin
Coagulation-fragmentation models: Well-posedness, Numerical approximations and Asymptotic analysis 24 Oct 2016 Partial Differential Equations NA SERB, India NA




Books

A. K. Giri : Mathematical and numerical for coagulation-fragmentation equations, VDM Verlag Dr. Mueller, Saarbuecken, Germany, ISBN-978-3639375244, PhD thesis, 2010

 

Publications

 

    Published/Accepted:

    1. The continuous collision-induced nonlinear fragmentation equation with non-integrable fragment daughter distributions, Journal of Differential Equations, 403, 235-271,2024 (with R. G. Jaiswal and Ph. Laurencot)
    2. A note on the Discrete Coagulation Equations with Collisional Breakage, Acta Applicandae Mathematicae, 189, 5, 2024 (with M. Ali)
    3. The discrete collision-induced breakage equation with mass transfer: well-posedness and stationary solutions, SIAM J. Math. Anal., 56 (3), 2915-2937, 2024 (with M. Ali and Ph. Laurencot)
    4. On the discrete Safronov-Dubovskiǐ coagulation equations: well-posedness, mass-conservation and asymptotic behaviour, Math. Meth. Appl. Sci. 47(6), 5191-5206, 2024 (with M. Ali and P. Rai)
    5. Well-posedness of the discrete collision-induced breakage equation with unbounded fragment distribution, Nonlinear Analysis: Real World Applications, 75, 103967, 2024 (with M. Ali and Ph. Laurencot)
    6. Numerical study of finite volume scheme for coagulation-fragmentation equations with singular rates, Journal of Hyperbolic Differential Equations, 20 (4), 793-823, 2023 (with S. K. Bariwal, P. K. Barik and R. Kumar)
    7. Convergence analysis of inexact Newton-Landweber iteration with frozen derivative in Banach spaces, J. Inverse and Ill-posed Problems, 2023, https://doi.org/10.1515/jiip-2023-0002(with G. Mittal)
    8. The continuous Redner-Ben-Avraham-Kahng coagulation system: well-posedness and asymptotic behaviour, Evolution Equations and Control Theory, 12(5), 1247-1267, 2023 (with P. Verma, F. da Costa)
    9. Instantaneous gelation and nonexistence of weak solutions for the Oort-Hulst-Safronov coagulation model, Proceedings of Royal Society London A, 479, 20220385, 2023 (with P. Rai, V. John)
    10. A modified steepest descent method for solving non-smooth inverse problems, Journal of Computational and Applied Mathematics, 424, 114997, 2023 (with G. Mittal)
    11. Improved local convergence analysis of Landweber iteration in Banach spaces, Archiv der Mathematik, 120, 195–202, 2023 (with G. Mittal)
    12. Nonstationary iterated Tikhonov regularization: Convergence analysis via Hölder stability, Inverse Problems, 38, 125008, 2022 (with G. Mittal)
    13. Global existence of solutions to the discrete Safronov–Dubovskii coagulation equations and failure of mass-conservation, J. Math. Anal. Appl, 519(1), 126755, 2023 (with M. Ali)
    14. Convergence Analysis of an optimally accurate frozen Multi-Level projected steepest descent Iteration for solving inverse problems, J. Complexity, 101711, 2022 (with G. Mittal)
    15. Convergence Analysis of iteratively regularized Gauss-Newton method with frozen derivative in Banach spaces, J. Inverse and Ill-posed Problems, 30(6), 857-876, 2022 (with G. Mittal)
    16. Novel multi-level projected iteration to solve inverse problems with nearly optimal accuracy, J. Optim. Theory Appl., 194:643–680, 2022 (with G. Mittal)
    17. 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)
    18. 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)
    19. Convergence rates for iteratively regularized Gauss-Newton method subject to stability constraints,J. Comput. Appl. Math., 400, Article No. 113744, 2022(with G. Mittal)
    20. A novel two-point gradient method for regularization of inverse problems in Banach spaces,Applicable Analysis, 101 (18), 6596-6622, 2022 (with G. Mittal)
    21. Existence and non-existence for collision-induced breakage equation, SIAM J. Math. Anal., 53(4), 4605--4636, 2021 (with Ph. Laurencot)
    22. Existence and uniqueness of weak solutions to the singular coagulation equation with collisional breakageNoDEA Nonlinear Differential Equations Appl., 28, Article No. 34, 2021(with P.K. Barik)
    23. Weak solutions to the collision-induced breakage equation with dominating coagulation, Journal of Differential Equations 288, 690-729, 2021 (with Ph. Laurencot)
    24. 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)
    25. Iteratively regularized Landweber iteration method: Convergence analysis via Holder Stability,Applied Mathematics and Computation, 392: Article No. 125744, 2021 (with G. Mittal)
    26. 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)
    27. 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)
    28. On Variational Regularization: Finite dimension and Holder stability, J. Inverse and Ill-posed Problems,29(2), 283-294, 2021(with G. Mittal)
    29. 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)
    30. Mass-Conserving solutions to the Smoluchowski coagulation equations with singular kernel,Proceedings of Royal Society Edinburgh, A 150(4), 1805-1825, 2020 ( with P.K. Barik and Ph. Laurençot)
    31. Generalized stochastic Burgers' equation with non-Lipschitz diffusion coefficient, Commun. Stoch. Anal., 12(3), 329-342, 2018 (with V. Kumar)
    32. 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)
    33. Convergence of the cell average technique for Smoluchowski coagulation equation, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 49 (2), 349-372, 2015(with A.K. Nagar)
    34. On the uniqueness for coagulation and multiple fragmentation equation, Kinetic and Related Models (KRM), 6(3), 589-599, 2013
    35. Stochastic Burger's equation with polynomial nonlinearity driven by Levy process, Commun. Stoch. Anal. (COSA), 7(1), 91-112, 2013 (with E. Hausenblas)
    36. 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)
    37. 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)
    38. Uniqueness for coagulation-fragmentation equations with strong fragmentation, Z. Angew. Math. Phys. (ZAMP), 62, 1047-1063, 2011 (with G. Warnecke)
    39. The continuous coagulation equation with multiple fragmentation, J. Math. Anal. Appl., 374: 71-87, 2011 (with J. Kumar and G. Warnecke) 

 

Honors And Awards
Honors
IMPRS, Otto-von-Guericke University, Magdeburg, Germany
2010
International Max-Planck Research School (IMPRS) Doctoral Fellowship
Chair for Applied Mathematics, Montan University Leoben, Austria
2012
FWF Austrian Science Funds Postdoctoral Fellowship
RICAM, Austrian Academy of Science, Linz, Austria
2014
Austrian Academy of Science Fellowship
MemberShips
SIAM
01 Jan 2018 - Present
Member
International Max-Planck Reseach Schools (IMPRS)
01 Oct 2007 - Present
Life Member
Teaching Engagements
Teaching Engagements
Theory of PDEs ( MAN-508 )
Spring
Theory of Partial Differential Equations ( MAN-518 )
Spring
Theory of Differential Equations ( MAN-903 )
Spring
Advanced Numerical Analysis/Finite Element Methods ( MAN-642/MAN-630 )
Autumn
Selected Topics in Analysis ( MAN-901 )
Spring
Functional Analysis ( MAN-611 )
Autumn
Mathematics I ( MA 001 )
Autumn
Real Analysis II ( MA 503 )
Autumn
Theory of Partial Differential Equations ( MA 506 )
Spring
Mathematical Methods ( MAN-002 )
Spring
Students
SuperVisions
Nonsingular and Singular Coagulation Models with Linear and Nonlinear Breakage
10 Jul 2014 - 18 Sep 2018
Other Supervisors: , Scholar: Prasanta Kumar Barik
On well-posedness for generalized stochastic Burgers-type equations
10 Jul 2014 - 12 Jun 2019
Other Supervisors: , Scholar: Vivek Kumar
Regularization for Nonlinear Inverse Problems via Stability Constraints
09 Jul 2016 - 02 May 2022
Other Supervisors: NA, Scholar: Gaurav Mittal
Oort-Hulst-Safronov coagulation model and its discrete counterpart with singular and nonsingluar unbounded coefficients
15 Jul 2015 - 10 Aug 2022
Other Supervisors: , Scholar: Pooja rai
Mathematical Theorey on the Discrete Collision-induced Breakage Equations and the Safronov- Dubovskii coagulation Equations
27 Dec 2017 - 05 Oct 2023
Other Supervisors: , Scholar: Mashkoor Ali
The Discrete and Continuous Redner-Ben-Avraham-Kahng Coagulation Models: Well-posedness, Large Time Behaviour an Their Connection
15 Sep 2018 - Present
Other Supervisors: , Scholar: Pratibha Verma
Associate Scholars
Pooja Rai
Population balance models
Mashkoor Ali
Semigroup theory for solving coagulation-fragmentation equations
Pratibha Verma
Studies of new models in population balance
Saroj si
Population Balance equations: Dynamics and Numerics
Ram Gopal Jaiswal
Indian Institute of Technology Roorkee
Self-similar and stationary solutions to coagulation-fragmentation equations
Miscellaneous
Events
West Asian Mathematical School on from Theorey to Simul"Recent Developments and Applications of PDEs
29 Aug 2019 - 03 Sep 2019
CIMPA, IMU, NBHM
GIAN Programme on Population Balance Equations with Applications
26 Nov 2018 - 30 Sep 2020
MHRD
Indo-French Research Workshop Theory and Simulation of Hyperbolic PDEs arising in Mathematical Biology and Fluid Flow
05 Jan 2019 - 11 Jan 2019
IFCAM
Visits
Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin, Germany
2019-06-22
DST-DAAD project visit for Scientific collaboration with Prof. Volker John
LAMA, University of Savoie Mont Blanc, Chambery, France
2022-12-02
Indo-French (IFCAM) project visit (with my three PhD students) for Scientific collaboration with Prof. Philippe Laurencot
Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin, Germany
2019-06-24
Workshop on Phase Transitions and Particle Systems
Instituto Politécnico de Bragança, Bragança, Portugal
2018-07-08
Invited Talk in ENSPM-2018
IST-Lisbon, Portugal
2018-07-01
Invited Lecture and Research Collaboration with Prof. Fernando da Costa
Université de Picardie Jules Verne LAMFA CNRS, Amiens - France
2018-06-20
Invited Lecture & Research Collaboration with Prof. Youcef Mammeri
Panjab Unversity, Chandigarh, India
2016-12-05
Invited talk in International Conference on Recent Advances in Theoretical and Computational Partial Differential Equations with Applications
Otto-von-Guericke University, Magdeburg, Germany
2016-09-08
Invited Talk in "Conference on Recent Advances in Analysis and Numerics of Hyperbolic Conservation Laws" (In the honor of 60th Birthday of Prof. Gerald Warnecke)
Max-Planck Institute, Leipzig, Germany
2016-09-06
invited lecture and scientific collaboration with Dr. Benjamin Gess
IIT Bhubaneswar
2016-07-25
Invited Lecture series in GIAN course on Modelling, Analysis and Simulation of Coagulant Fluid
IISER Thiruvananthapuram
2016-06-06
Invited Lecture Series in a Workshop on High Performance Scientific Computing
South Asian University, New Delhi, India
2015-12-28
Invited talk in "International Conference on Current Trends in PDEs: Theory and Computation"
TIFR-CAM, Banalore, India
2015-12-21
Invited Talk in "Conference on Computational PDEs"
University of Porto, Portugal
2015-06-10
Contributed talk in the "joint International Meeting of AMS/EMS/SPM 2015"
Administrative Positions
Warden
01 Jul 2021 - 30 Jun 2022
Ganga Bhawan
Chief Warden
01 Jul 2022 - 30 Jun 2023
Ganga Bhawan
Department Faculty Committee Secretary
01 Sep 2020 - 31 Aug 2022
Department of Mathematics, IIT Roorkee
Coordinator for Mathematics-I
15 Nov 2020 - 15 May 2021
IIT Roorkee
Faculty Advisor Placement
15 Jul 2021 - Present
Department of Mathematics
Convener
01 Jan 2015 - 31 Dec 2017
Department Faculty Search Committee (DFSC)
OC website (Department)
01 Sep 2018 - 31 Aug 2020
IIT Roorkee
Warden
01 Jun 2017 - 30 Jun 2020
Cautley Bhavan
International Scientific Visitors
  1. Prof. Philippe Laurencot, CNRS, University of Toulouse, France, Research collaboration and Invited Lecture Series under Indo-French research proect funded by IFCAM (24/02/2022-23/03/2022)
  2. Prof. Philippe Laurencot, CNRS, University of Toulouse, France, Research collaboration and Invited Lecture Series under Indo-French research proect funded by IFCAM (26/02/2020-20/03/2020)
  3. Prof. Volker John, Weierstass Institute for Applied Analysis and Stochastics (WIAS) and Freie Unversity Berlin, Germany Research Collaboration and Invited Lecture Series under Indo-German research project funded by DST-DAAD (21/01/2020-31/01/2020)
  4. Prof. Fernando da Costa, IST Lisbon and University of Aberta Lisbon, Portugal, Research collaboration and Invited speaker in West Asian Mathematical School funded by CIMPA, IMU and NBHM (25/08/2019-04/09/2019)
  5. Prof. Michael Grinfeld, University of Strathclyde, Glasgow, UK, Research collaboration and Invited speaker in West Asian Mathematical School funded by CIMPA, IMU and NBHM (25/08/2019-02/09/2019)
  6. Prof. Youcef Mammeri, LAMFA, CNRS, University of Picardie Jules Verne, Amiens, France, Research collaboration and Invited speaker in West Asian Mathematical School funded by CIMPA, IMU and NBHM (28/08/2019-04/09/2019)
  7. Prof. Joaquim Correia, University of Evora, Portugal, Co-organizer and Invited speaker in West Asian Mathematical School funded by CIMPA, IMU and NBHM (25/08/2019-04/09/2019)
  8. Prof. Nabil Badjaoui, LAMFA, CNRS, University of Picardie Jules Verne, Amiens, France, Research Collaboration and and Invited speaker in West Asian Mathematical School funded by CIMPA, IMU and NBHM (28/08/2019-04/09/2019)
  9. Prof. Marilia Pires, University of Evora, Portugal, Research Collaboration and Invited speaker in West Asian Mathematical School funded by CIMPA, IMU and NBHM (25/08/2019-04/09/2019)
  10. Prof. Fernando da Costa, IST Lisbon and University of Aberta Lisbon, Portugal, Research collaboration and Invited Lecture Series (13/01/2019-25/01/2019)
  11. Prof. Youcef Mammeri, LAMFA, CNRS, University of Picardie Jules Verne, Amiens, France, Research Collaboration and Invited Lecture (13/01/2019-16/01/2019)
  12. Prof. Nabil Badjaoui, LAMFA, CNRS, University of Picardie Jules Verne, Amiens, France, Research Collaboration and Invited Lecture (13/01/2019-16/01/2019)
  13. Prof. Marilia Pires, University of Evora, Portugal, Research Collaboration and Invited Lecture (13/01/2019-16/01/2019)
  14. Prof. Jacek Banasiak, University of Pretoria, South Africa, GIAN Program and Research collaboration (19/11/2018-01/12/2018)
Referee for International Journals
  • SIAM Journal of Applied Mathematics
  • IMA Journal of Numerical Analysis
  • Mathematical Reviews/MathSciNet (AMS)
  • Proceedings of the Royal Society A
  • Journal of European Mathematical Society
  • Journal of Numerical Mathematics
  • Proceedings of the National Academy of Sciences
  • Mathematical Methods in the Applied Sciences
  • Mathematical Modelling and Analysis
  • Korean Journal of Chemical Engineering
  • Differential Equations and Dynamical Systems
  • Applications of Mathematics
  • Inverse Problems and Imaging
  • Journal of Mathematical Analysis and Applications
  • Z. Angew. Math. Phys. (ZAMP)
  • Studies in Applied Mathematics
  • Journal of Global Optimization
  • Acta Applicandae Mathematicae
  • Inverse Problems