A. K. Nandakumaran, Professor

Room No: N-27
Department of Mathematics
Indian Institute of Science
Bangalore- 560 012, India

 



Publications

  • Book: A. K. Nandakumaran, P. S. Datti, Raju K. George, Ordinary Differential Equations: Principles and Application, (Cambridge-IISc Series), Cambridge University Press (2017).
  • Book: 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), Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem, to appear ESAIM:COCV.
  • (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. pdf file
  • (with S Aiyappan and Abu Sufian), Asymptotic analysis of Boundary Optimal ControlProblem on a General Branched Structure, Mathematical Methods in the Applied Sciences, 1-28 (2019). DOI: 10.1002/mma.5748.pdf file
  • (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.pdf file
  • (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). DOI: 10.1007/s10231-019-00848-7pdf file
  • (with S Aiyappan and Ravi Prakash), Semi-linear optimal control problem on a smoothoscillating domain, Communications in Contemporary Mathematics, 1-26 (2019). DOI:10.1142/S0219199719500299.pdf file
  • (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), DOI: 10.3233/ASY-191526. pdf file
  • (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) https://doi.org/10.1007/s00245-018-9499-4 (34 pages) pdf file
  • (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. pdf file
  • (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. pdf file
  • (with Sudipto Chowdhury and Thirupathi Gudi), Error Bounds for a Dirichlet Boundary Control Problem Based on Energy Spaces, Math. Comp. 86 (2017), 1103-1126. pdf file
  • (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. pdf file
  • (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. pdf file
  • (with Sudipto Chowdhury and Thirupathi Gudi), A Frame Work 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). pdf file
  • (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). pdf file.

  • (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. pdf file
  • (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. pdf file.

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

  • (with Ravi Prakash and J P Raymond), Asymptotic analysis of the interior optimal control associated to Stokes' system in a domain with oscillating boundary, Numerical Functional Analysis and Applications, 35(3): 323 – 355, 2014. pdf file.

  • (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.pdf file.

  • (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. pdf file.

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

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

  • (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. pdf file.

  • (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.pdf file.

  • (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.pdf file.

  • (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.pdf file.

  • (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.pdf file.

  • (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.pdf file.

  • (with M. Muslim and Carlos Conca), Approximation of Solutions to Fractional Integral Equations, Computers and Mathematics with Applications (Elsvier), 59 (2010) 1236-1244. pdf file.

  • (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.pdf file.

  • (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.pdf file.

  • (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.pdf file.

  • (with S. Panigrahi), Oscillation Criteria for Differential Equations of Second Order, Mathematica Slovaca (Springer Journal), Vol. 59, 2009, No. 4, 433-454.pdf file.

  • (Hari 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.pdf file.

  • (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.pdf file.

  • (with T. Muthukumar) Homogenization of some Low-Cost Control Problems on Perforated Domains, J. Math. Anal. Appl. 351 (2009) 29-42.pdf file.

  • (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.pdf file.

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

  • (T. Muthukumar) Darcy-type law associated to an optimal control problem, E. journal of Differential Equations, Vol. 2008, No. 16, pp. 1-12.pdf file.

  • (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.pdf file.

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

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

  • (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).pdf file.

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

  • (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.pdf file.

  • (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.pdf file.

  • (with Raju K. George), Exact Controllability of a Semi Linear Thermoelastic System, Numerical Functional Analysis and Optimization, 25 (2004), No. 3-4, 271-285.pdf file.

  • (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.pdf file.

  • 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.pdf file.

  • (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.pdf file.

  • (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.pdf file.

  • Convergence of 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.pdf file.

  • (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.pdf file.

  • (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. pdf file.

  • (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.>pdf file.

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

  • (with Raju George and Arapostatis), A Note Controllability of Impulsive Systems, J. Math. Anal. and Appl., 241, (2000), pp 276-283.pdf file.

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

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

  • (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.>pdf file.

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

  • (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.pdf file.

  • 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. pdf file.

Proceedings

  • 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. pdf file.

  • (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).pdf file.

General Articles