Books

1. [A. K. Nandakumaran, P. S. Datti, Raju K. George], Ordinary Differential Equations: Principles and Application,
   Cambridge-IISc Series, Cambridge University Press (2017).


2. [A. K. Nandakumaran, P. S. Datti], Partial Differential Equations: Classical Theory with a Modern Touch,
   Cambridge-IISc Series, Cambridge University Press (2020).



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Journal Articles

1. [with Abu Sufian and Renjith T], Homogenization of Semi-linear Optimal Control Problems on Oscillating Domains with Matrix Coefficients, Applied Mathematics & Optimization,(2024) 89:46 (42 pages).


2. [with Abu Sufian], Unfolding Operator on Heisenberg Group, SIAM J. of Control and Optimization, Vol 61, No. 3, pp. 1350-1374.


3. [with Abu Sufian and Renjith T], Homogenization of elliptic PDE with L1 source term in domains with boundary having very general oscillations, Asymptotic Analysis 133 (2023) 123-158.


4. [with Abu Sufian and Renjith T], Homogenization with strong contrasting diffusivity in a circular oscillating domain with L1 source term, Annali di Matematica Pura ed Applicata(1923 -)


5. [with K. Sankar], Homogenization of the heat equation in a noncylindrical domain with randomlyoscillating boundary, Math Meth Appl Sci. (2022), 1–24.


6. [with S. Monsurro and C. Perugia], Exact Internal Controllability for Evolutionary Imperfect Transmission Problems, Applied Mathematics and Optimization, (2022) 85:40, 33pages.


7. [with S. Monsurro and C. Perugia], Exact Boundary Controllability for Evolutionary Imperfect Transmission Problems, Ricerche di Matematica.


8. [with Abu Sufian], Strong Contrasting Diffiusivity in General Oscillating Domains: Homogenization of Optimal Control Problems, Journal of Differential Equations 291(2021) 57–89.


9. [with Abu Sufian], Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem, ESAIM: COCV 27 (2021) S4.


10. [with K. Murali, Hari M Varma], On the equivalence of speckle contrast-based and diffuse correlation spectroscopy methods inmeasuring in vivo blood flow, Optics Letters 3993, Vol. 45, No. 14 / 15 July 2020.


11. [with S Aiyappan and Abu Sufian], Asymptotic analysis of a Boundary Optimal Control Problem on a General Branched Structure, Mathematical Methods in the Applied Sciences, 1-28 (2019).


12. [with K. Murali, Turgurt Durduran, Hari M Varma], Recovery of the diffuse correlation spectroscopy data-type from speckle contrast measurements: towards low-cost, deep-tissue blood flow measurements, Biomedical Optics Express 5395, Vol. 10, No. 10 / 1 October 2019.


13. [with S Aiyappan and Ravi Prakash], Locally Periodic Unfolding Operator for Highly Oscillating Rough Domains, Annali di Matematica Pura ed Applicata, Vol. 198(6), pp. 1931-1954 (2019).


14. [with S Aiyappan and Ravi Prakash], Semi-linear optimal control problem on a smoothoscillating domain, Communications in Contemporary Mathematics, 1-26 (2019).


15. [with S Aiyappan, Editha C. Jose and Ivy Carol B. Lomerio], Control Problem on a Rough Circular Domain and Homogenization, Asymptotic Analysis, Vol. 115, no. 1-2, pp. 19-46 (2019).


16. [with Rajesh Mahadevan and Ravi Prakash], Homogenization of an elliptic equation in a domain with oscillating boundary with non-homogeneous non-linear boundary conditions, Appl. Math. Optim.(2018).


17. [with S. Aiyappan and Ravi Prakash], Generalization of Unfolding Operator for Highly Oscillating Smooth Boundary Domains and Homogenization, Calculus of Variations and PDE (2018) 57-86.


18. [with S. Aiyappan], Optimal Control Problem in a Domain with Branched Structure and Homogenization, Mathematical Methods in Applied Sciences, Volume 40, Issue 8, 30 May (2017), Pages: 3173–3189.


19. [with Sudipto Chowdhury and Thirupathi Gudi], Error Bounds for a Dirichlet Boundary Control Problem Based on Energy Spaces, Math. Comp. 86 (2017), 1103-1126.


20. [with Ravi Prakash and Bidhan Chandra Sardar], Asymptotic analysis of Neumann periodic optimal boundary control problem, Mathematical Methods in Applied Sciences, (2016), 39 4354 – 4374.


21. [with Ali Sili], Homogenization of a Hyperbolic Equation with Highly Contrasting Diffusivity Coefficients, Differential and Integral Equations, Volume 29, Numbers 1-2 (2016), 37-54.


22. [with Sudipto Chowdhury and Thirupathi Gudi], A FrameWork for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to $C^0$ IP methods , Numerical Functional Analysis and Optimization, 36: 1388-1419, (2015).


23. [with Ravi Prakash and Bidhan Chandra Sardar], Periodic Controls in an Oscillating Domain: Controls via Unfolding and Homogenization, SIAM Journal on Control and Optimization, Vol. 53, No. 5, pp. 3245-3269 (2015).


24. [with Umberto De Maio and Carmen Perugia], Exact Internal Controllability for the Wave Equation in a Domain with Oscillating Boundary with Neumann Boundary Condition, Evolution Equation and Control Theory, Vol. 4, No. 3 (2015), pp. 325-346.


25. [with K. P. Mohanan, R. M. Vasu and D. Roy], Ultrasound-modulated optical tomography: Direct recovery of elasticity distribution from experimentally measured intensity autocorrelation, Vol. 32, No. 5 / May 2015 / Journal of the Optical Society of America A, 955-963.


26. [with Augusto Visitin], Variational Approach to Homogenization of Doubly-Nonlinear Flow in a Periodic Structure, Nonlinear Analysis, TMA, 120(2015) 14-29.


27. [with Ravi Prakash and J P Raymond],Stokes’ System in a Domain with Oscillating Boundary: Homogenization and Error Analysis of an Interior Optimal Control Problem, Numerical Functional Analysis and Applications, 35(3): 323 – 355, 2014.


28. [with K. P. Mohanan, D. Roy and R. M. Vasu], Quantitative Ultrasound-modulated Optical Tomography: A direct Gauss-Newton approach to recover elasticity distribution from the measured intensity autocorrelation, Neural, Parallel and Scientific Computations 21 (2013) 319-334.


29. [with Ravi Prakash and Bidhan Chandra Sardar],Homogenization of an optimal control problem in a domain with highly oscillating boundary using periodic unfolding method, MESA, Vol. 4, No. 3 (2013), 281-303.


30. [with Ravi Prakash], Homogenization of Boundary Optimal Control Problems with Oscillating Boundaries, Nonlinear Studies Vol. 20, No. 3, pp. 1-25, (2013).


31. [with U. De Maio],Exact Internal Controllability for a Hyperbolic Problem in a Domain with Highly Oscillating Boundary , Asymptotic Analysis, 83 (2013) 189-206.


32. [with N. Hyvonen, Hari M Varma and R. M. Vasu], Generalized eigenvalue decomposition of the field autocorrelation in correlation diffusion of photons in turbid media, Mathematical Methods in Applied Sciences, (2013), 36, 1447-1458.


33. [with Ravi Prakash and J P Raymond], Asymptotic Analysis and Error Estimates for an Optimal Control Problem with Oscillating Boundaries, Ann Univ Ferrara (2012) 58:143–166.


34. [with Hari. M. Varma and R. M. Vasu], Analysis of the inverse problem associated with diffuse correlation tomography, Mathematics in Science, Engineering and Aerospace (MESA), Vol. 3, No. 1 (2012) 79-97.


35. [with M. Tadi and S. S. Sritharan], An Inverse Problem for Helmholtz Equation, Inverse Problems in Science and Engineering, Volume 19, Issue 6, (2011) 839-854.


36. [with Hari. M. Varma, K.P. Mohanan, N. Hyvonen and R. M.Vasu], Ultrasound-modulated optical tomography: Recovery of amplitude of vibration in the insonified region from boundary measurement of light correlation, J. Opt. Soc. Am. A, Vol. 28, No. 11 / November 2011.


37. [with D.N. Chalishajara, R. K.George and F.S. Acharya], Trajectory controllability of nonlinear integro-differential system , Journal of the Franklin Institute 347(2010) 1065–1075.


38. [with M. Muslim and Carlos Conca], Approximation of Solutions to Fractional Integral Equation, Computers and Mathematics with Applications (Elsvier), 59 (2010) 1236-1244.


39. [with M. Muslim], Existence and approximations of solutions to some fractional order functional integral equations, Journal of Integral Equations and Applications, Volume 22, Number 1, 2010, 95-114.


40. [with Hari M Varma, B. Banerjee, D. Roy and R. M. Vasu], Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography , J. Opt. Soc. Am. A, Vol. 27, No. 2/February 2010.


41. [with H.M. Verma, B. Banerjee, R. M. Vasu and D. Roy], Pseudo-time marching schemes for inverse problems in structural health assessment and medical imaging, Current Science, Vol. 97, No. 8, 25 October 2009.


42. [with S. Panigrahi], Oscillation Criteria for Differential Equations of Second Order, Mathematica Slovaca (Springer), Vol. 59, 2009, No. 4, 433-454.


43. [with M Varma and R. M. Vasu], Study of turbid media with light: Recovery of mechanical and optical properties from Boundary measurement of intensity autocorrelation of light, J. Opt. Soc. Am. A / Vol. 26, No. 6 / June 2009.


44. [with M. Muslim and Ravi. P. Agarwal], Existence, uniqueness and convergence of approximate solutions of impulsive neutral differential equations, International Journal of Functional Differential Equation, Volume 16, No. 3 (2009) pp 529-544.


45. [with T. Muthukumar], Homogenization of Low-Cost Control Problems on Perforated Domains, J. Math. Anal. Appl. 351 (2009) 29-42.


46. [with M. Muslim and Ravi. P. Agarwal], Existence of Local and Global Solutions to Fractional Order Integral Equations, PanAmerican Mathematical Journal, Volume 18(2008), Number 3, 47-57.


47. An overview of Homogenization, Journal of IISc., Vol. 87, No. 4, Oct-Dec. 2007. (Review article).


48. [T. Muthukumar], Darcy-type law associated to an optimal control problem, E. journal of Differential Equations, Vol. 2008, No. 16, pp. 1-12.


49. [Hari M. Varma and R. M. Vasu],Direct reconstruction of complex refractive index distribution from boundary measurement of intensity and normal derivative intensity, J. Opt. Soc. Am. A, Vol 24, No.10, October 2007, pp. 3089-3099.


50. [D. N. Chalishajar, R. K. George],Exact Controllability of the nonlinear third order dispersion equation, J. Math. Anal. Appl. 332(2007) 1028-1044.


51. [P. Dhanumjaya], Orthogonal Cubic Spline Collocation Method for the Cahn-Hilliard Equation, Applied Mathematics and Computation, 182(2006) 1316-1329.


52. [with D. N. Chalishajar and Raju K. George], Exact controllability of generalized Hammerstein type equation, Industrial Mathematics, Edited by M. C. Joshi, A. K. Pani and A . V. Sabnis, Narosa Publishing House, New Delhi, pp. 61-70 (2006).


53. [with P. K. Ratnakumar], Schrodinger equation and the oscillatory semigroup for the Hermite operator, Journal of Functional Analysis, 224(2005)371-385.


54. [with M. K. Ghosh, K. Sureshkumar and K. S. Mallikarjuna Rao], Differential Games of Fixed Duration in the Framework of Relaxed Startegies}, Differential Equations and Dynamical Systems , Vol.13, Nos. 3 & 4, July & October, 2005, pp. 251-273.


55. [D. N. Chalishajar, Raju K. George], Exact Controllability of second order semi-linear neutral functional differential inclusions in Banach spaces, Mediterrian Journal of Mathematics 1(2004), No. 4, 463-477.


56. [with Raju K. George], Exact Controllability of a Semilinear Thermoelastic System , Numerical Functional Analysis and Optimization, 25 (2004), No. 3-4, 271-285.


57. [with M. Rajesh, K. S. Mallikarjuna Rao], An Example in the homogenization of a degenerate elliptic equation, Asymptotic Analysis, V36, Nos. 3-4 (2003), 187-201.


58. Homogenization of Certain Spectral Problems, Proceedings of the International Conference on Linear Algebra, Numerical Analysis and Wavelet Analysis (Aug. 6 -15, 2001), Allied Publishers (p) LTD. New Delhi (2003), 147-165.


59. [with M. K. Ghosh and K.S.Mallikarjuna Rao], A Zero Sum Differential Game in a Hilbert Space, J. Math. Anal. Appl. 283 (2003) 167-179.


60. [with M. Rajesh], Homogenization of a parabolic equation in perforated domain with Dirichlet boundary condition, Proc. Indian Acad. Sci. (Math. Sci.), Vol.112, No. 3, August 2002, pp.425-439.


61. Convergence of the Boundary control for the wave equation in domains with holes of critical size, E. journal of Differential Equations, Vol. 2002(2002), No. 35, pp. 1-10.


62. [with M. K. Ghosh, K. S. Mallikarjuna Rao and K. Sureshkumar], Viscosity solution of Second Order HJI equation and Application to zero sum Stochastic differential Game, Advances in Probability and Stochastic Processes, Notable Publications, Inc. New Jersey, USA, 2001 PP. 51 - 63.


63. [with M. Rajesh],Homogenization of a parabolic equation in perforated domain with Neumann boundary condition, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 112, No. 1, February 2002, pp.195-207.


64. [with M. K. Ghosh, K. Sureshkumar and K. S. Mallikarjuna Rao], A Note on Stochastic Minimax Principle, Differential Equations and Dynamical Systems, V9, Nos. 1 & 2, January and April (2001) pp. 105-112.


65. [with M. Rajesh],Homogenization of a nonlinear degenerate parabolic differential equation, Electronic J. of Differential Equations 2001(2001), No. 17, pp 1-19.


66. [with Raju George and Arapostatis], A Note on Controllability of Impulsive Systems, J. Math. Anal. and Appl., 241, (2000), pp 276-283.


67. Stackelberg optimization with microstructure and homogenization, Diff. Equ. and Dyn. Sys. V6, Nos.1 \& 2, Jan-Apr.(1998), pp 113-123.


68. [with Raju George], Partial Exact controllability of a linear thermoelastic system, Indian J. of Mathematics, V37, N2 (1996), pp 165-171.


69. [with Raju George], Partial Exact controllability of a Nonlinear system, Revista Matematica de la Universidad Complutense de Madrid, Volumen 8, Numero 1:1995, pp 181-195.


70. Homogenization of Eigenvalue Problems of Elasticity in perforated Domain, Asymptotic Analysis, 9(1994) 337-358.


71. [with G. Allaire and F. Murat] Homogenization with Neumann Boundary Condition on the holes and a Dirichlet Condition on the exterior Boundary, Asymptotic Analysis, 7 (1993) 92-95.


72. Steady and Evolution stokes Equations in a Porous Media with Nonhomogenous Boundary Data: A Homogenization Process, Differential and Integral Equation, Vol. 5, No. 1, January 1992, pp. 73-93.