Department of Mathematics

Indian Institute of Science

Bangalore- 560 012, India

**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 Control****Problem 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.

**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.

**A View of Newton as
a Mathematician**, Resonance,
December 2006. pdf file.