*[A. K. Nandakumaran, P. S. Datti, Raju K. George],*Ordinary Differential Equations: Principles and Application,

Cambridge-IISc Series, Cambridge University Press (2017).*[A. K. Nandakumaran, P. S. Datti],*Partial Differential Equations: Classical Theory with a Modern Touch,

Cambridge-IISc Series, Cambridge University Press (2020).

*[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).*[with Abu Sufian]*, Unfolding Operator on Heisenberg Group, SIAM J. of Control and Optimization, Vol 61, No. 3, pp. 1350-1374.*[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.*[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 -)*[with K. Sankar],*Homogenization of the heat equation in a noncylindrical domain with randomlyoscillating boundary, Math Meth Appl Sci. (2022), 1–24.*[with S. Monsurro and C. Perugia],*Exact Internal Controllability for Evolutionary Imperfect Transmission Problems, Applied Mathematics and Optimization, (2022) 85:40, 33pages.*[with S. Monsurro and C. Perugia],*Exact Boundary Controllability for Evolutionary Imperfect Transmission Problems, Ricerche di Matematica.*[with Abu Sufian],*Strong Contrasting Diffiusivity in General Oscillating Domains: Homogenization of Optimal Control Problems, Journal of Differential Equations 291(2021) 57–89.*[with Abu Sufian],*Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem, ESAIM: COCV 27 (2021) S4.*[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.*[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).*[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.*[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).*[with S Aiyappan and Ravi Prakash],*Semi-linear optimal control problem on a smoothoscillating domain, Communications in Contemporary Mathematics, 1-26 (2019).*[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).*[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).*[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.*[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.*[with Sudipto Chowdhury and Thirupathi Gudi],*Error Bounds for a Dirichlet Boundary Control Problem Based on Energy Spaces, Math. Comp. 86 (2017), 1103-1126.*[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.*[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.*[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).*[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).*[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.*[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.*[with Augusto Visitin],*Variational Approach to Homogenization of Doubly-Nonlinear Flow in a Periodic Structure, Nonlinear Analysis, TMA, 120(2015) 14-29.*[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.*[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.*[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.*[with Ravi Prakash],*Homogenization of Boundary Optimal Control Problems with Oscillating Boundaries, Nonlinear Studies Vol. 20, No. 3, pp. 1-25, (2013).*[with U. De Maio],*Exact Internal Controllability for a Hyperbolic Problem in a Domain with Highly Oscillating Boundary , Asymptotic Analysis, 83 (2013) 189-206.*[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.*[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.*[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.*[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.*[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.*[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.*[with M. Muslim and Carlos Conca],*Approximation of Solutions to Fractional Integral Equation, Computers and Mathematics with Applications (Elsvier), 59 (2010) 1236-1244.*[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.*[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.*[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.*[with S. Panigrahi],*Oscillation Criteria for Differential Equations of Second Order, Mathematica Slovaca (Springer), Vol. 59, 2009, No. 4, 433-454.*[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.*[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.*[with T. Muthukumar],*Homogenization of Low-Cost Control Problems on Perforated Domains, J. Math. Anal. Appl. 351 (2009) 29-42.*[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.- An overview of Homogenization, Journal of IISc., Vol. 87, No. 4, Oct-Dec. 2007. (Review article).
*[T. Muthukumar],*Darcy-type law associated to an optimal control problem, E. journal of Differential Equations, Vol. 2008, No. 16, pp. 1-12.*[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.*[D. N. Chalishajar, R. K. George],*Exact Controllability of the nonlinear third order dispersion equation, J. Math. Anal. Appl. 332(2007) 1028-1044.*[P. Dhanumjaya],*Orthogonal Cubic Spline Collocation Method for the Cahn-Hilliard Equation, Applied Mathematics and Computation, 182(2006) 1316-1329.*[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).*[with P. K. Ratnakumar],*Schrodinger equation and the oscillatory semigroup for the Hermite operator, Journal of Functional Analysis, 224(2005)371-385.*[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.*[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.*[with Raju K. George],*Exact Controllability of a Semilinear Thermoelastic System , Numerical Functional Analysis and Optimization, 25 (2004), No. 3-4, 271-285.*[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.- 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.
*[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.*[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.- 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.
*[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.*[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.*[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.*[with M. Rajesh],*Homogenization of a nonlinear degenerate parabolic differential equation, Electronic J. of Differential Equations 2001(2001), No. 17, pp 1-19.*[with Raju George and Arapostatis],*A Note on Controllability of Impulsive Systems, J. Math. Anal. and Appl., 241, (2000), pp 276-283.- Stackelberg optimization with microstructure and homogenization, Diff. Equ. and Dyn. Sys. V6, Nos.1 \& 2, Jan-Apr.(1998), pp 113-123.
*[with Raju George],*Partial Exact controllability of a linear thermoelastic system, Indian J. of Mathematics, V37, N2 (1996), pp 165-171.*[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.- Homogenization of Eigenvalue Problems of Elasticity in perforated Domain, Asymptotic Analysis, 9(1994) 337-358.
*[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.- 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.

- Homogenization and Applications to Stokes Equations, National conference on Fluid Flow and Control, March 27-28, 2003. Asymptotic Analysis of Viscosity Solutions, National conference on Recent Trends in Applied mathematics, April 25-28, 2003.
- Exact Controllability of Linear Wave Equation and Hilbert Uniqueness method, National Conference On recent trends in Computational Mathematics(2004), Computational Mathematics, Narosa Publishing House (2005), pp9-18.
- An overview of Homogenization, Journal of IISc., Vol 87, No. 4, oct-Dec. 2007.
*[Hari M Varma and R. M. Vasu]*Direct reconstruction of complex refractive index distribution from boundary measurements, PAMM, Proc. Appl. Math. Mech. 7, 2010017–2010018 (2007).

- The Meaning of Integration I, Resonance, April 2004.
- The Meaning of Integration II,
*Resonance*, May 2004. - A View of Newton as a Mathematician, Resonance, December 2006.

© A.K. Nandakumaran. All Rights Reserved. Designed by Shanmugavel