International Centre for Theoretical Sciences, Bengaluru
Area of Research:  Partial Differential Equations, Control Theory and Fluid flow problems.
  +91 80 4653 6150
  mythily ictsresin

2020-2022

  1. (with Debayan Maity and Debanjana Mitra) Lack of complete stabilizability of some coupled ODE-Parabolic systems. To appear in the special issue of Mathematics Reports, dedicated to Marius Tucsnak on the occasion of his 60th birthday.
  2. Invitation to Differential Equations, The Mathematics Student, Vol. 90, Nos. 1-2, January-June (2021), 6375 
  3. (with P. Chandrashekhar, J-P Raymond, Ruchi Sandilya) Numerical stabilization of the Boussinesq system using boundary feedback control , Computers and Mathematics with Applications, 89 (2021), 163 -183. 
  4. (with S. Ne ̆casova ́ , A.Roy, A. Schlo ̈merkemper) Self-propelled motion of a rigid body inside a density dependent incompressible fluid, Mathematical Modelling of Natural Phenomena, 16 (2021) 9, 1- 26. 
  5. (with Mehdi Badra, Debanjana Mitra, Jean Pierre Raymond) Local feedback stabilization of of time-periodic evolution equations by finite dimensional controls, ESAIM Control Optim. Calc. Var. 26 (2020), Paper No. 101, 38 pp 
  6. (with Mehdi Badra, Debanjana Mitra, Jean Pierre Raymond) Stabilizability of time- periodic evolution equations by finite dimensional controls, SIAM J. Control Optim. 58(2020), No. 3, 1735-1768. 
  7. ( with Takeo Takahashi, Arnab Roy) Remark on the global null controllability for a viscous Burgers - particle system with particle supported control, Applied Mathematics Letters, Vol 107, September 2020, 7pp. 

2010-2020

  1. (with Debanjana Mitra, Michael Renardy), Pure Stress modes for linear viscoelastic flows with variable coefficients, Z. Angew. Math. Phys.Vol 70, (2019) , 76-86. 
  2. (with Jean-Pierre Raymond and Arnab Roy), Boundary feedback stabilization of the Boussinesq system with mixed boundary conditions, Jl. Diff. Equns. 266 (2019), 4268 - 4304. 
  3. (with Apte, Amit; Auroux, Didier ) Observers for compressible Navier-Stokes equation. SIAM J. Control Optim. 56 (2018), no. 2, 1081-1104. 
  4. ( with Debanjana Mitra and Michael Renardy), Approximate controllability results for viscoelastic flows with infinitely many relaxation modes, Jl. Diff. Equns., Volume 264, Issue 2, 15 January 2018, Pages 575-603.
  5. (with Debanjana Mitra and Jean-Pierre Raymond), LocalstabilizationofCompressible Navier-Stokes equations in one dimension around nonzero velocity, Advances in Diff. Equns. Vol 22,No. 9-10 (2017) 693-736. 
  6. ( with Debanjana Mitra and Michael Renardy), Interior local null Controllability of one dimensional Compressible flow near a constant steady state, Mathematical Methods in Applied Sciences, 40(2017), No. 10, 3445-3478. 
  7. ( with Shirshendu Chowdhury, Debanjana Mitra and Michael Renardy), Approximate Controllability results for Linearized visco-elastic flows, Jl. Math. Fl. Mech. 19 (2017), No. 3, 529-549. 
  8. (with G.Canevari and Apala Majumdar) Radial symmetry in three dimensional shells in Landau-de Gennes theory, Physica D, 314 (2016), 18-34. 
  9. (with Debanjana Mitra and Jean-Pierre Raymond) Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension, Math. Control Relat. Fields, 5 (2015), no. 2, 259-290. 
  10. (with Shirshendu Chowdhury, Debayan Maity and Jean-Pierre Raymond) Local Stabilization of Compressible Navier Stokes System around a null velocity in One Dimension, Jl. Differential Equns. 259 (2015) 371-407. 
  11. (with Eunkyoung Ko and R. Shivaji) Uniqueness of positive radial solutions for a class of semipositone problems on the exterior of a ball, Jl Math. Analysis and Applications, 423 (2015), no. 1, page 399-409. 
  12. ( with Shirshendu Chowdhury, Debanjana Mitra and Michael Renardy) Null Control- lability of the Linearized Compressible Navier Stokes System in One Dimension, Jl. Differential Equns. 257 (2014) , page 3813–3849. 
  13. (with Sanjiban Santra) Uniqueness and profile of positive solutions of a critical exponent problem with Hardy potential, J. Diffl. Equns, 254 (2013), page 4347-43. 
  14. (with Shirshendu Chowdhury) Optimal Control of Linearized Compressible Navier- Stokes Equations, ESIAM : COCV - Control, Optimization and Calculus of Variations, 19(2013), page 587-615. 
  15. (with Shirshendu Chowdhury, Jean-Pierre Raymond) Controllability and Stabilizability of linearized Compressible Navier Stokes System in one dimension, SIAM Jl. Con- trol and Optim., Vol 50, No. 5 (2012), page 2959-2987. 
  16. ( with Amit Apte, Didier Auroux) Variational data assimilation for discrete Burgers equation. Proceedings of the Eighth Mississippi State-UAB Conference on Differential Equations and Computational Simulations, 1530, Electron. J. Differ. Equ. Conf., 19, 2010. 
  17. (with G. Barles and S. Dharmatti) Hybrid control problems with unbounded cost, ESAIM Control Optim. Calc. Var. 16 (2010), no. 1, 176–193. 

2000-2009

  1. (with T.V.Anoop and M. Lucia ) Weighted eigenvalue problems with weights in Lorentz spaces, Calc. Var. Partial Differential Equations 36 (2009), no. 3, 355–376. 
  2. (with A.J.Shaiju) Construction of Approximate Optimal Strategies for Differential Games in a Hilbert Space, Journal of Optimization Theory and Applications, vol 141, 2, 2009, page 349-370. 
  3. ( with Marcello Lucia ) Global Bifurcation for semilinear problems, Recent advances in Nonlinear Analysis, Ed. Chipot, C-S Lin, D-H Tsai, World Scientific, pp 197-216, (2007) 
  4. (with R.Shivaji, Jinglong Ye) “Positive Solutions for a class of infinite semipositone problems “, Differential and Integral Equations, Volume 20, Number 12, 1423-1433, (2007). 
  5. (with J.Giacomoni and J.Prajapat) Positive solutions for elliptic problems with critical indefinite nonlinearity in bounded domains, Electronic Journal of Differential Equa- tions, Conf. 15 (2007), 107-126. 
  6. (with Jaffar Ali and R. Shivaji) Multiple positive solutions for classes of elliptic systems with combined nonlinear effects, Diff and Integ. Equns., Vol 19, No. 6 (2006), 660-680. 
  7. (with Dharmatti Sheetal) Uniqueness of Unbounded Viscosity Solutions for Impulse Control Problems , Jl. Math Anal. Appl, Vol 315,2, 2005, 686-710. 
  8. (with Dharmatti Sheetal) Hybrid Control and Viscosity Solutions, SIAM Jl Control and Opt.,vol 44, No 4, 2005, 1259-1288. 
  9. (with J.Giacomoni and J.Prajapat) Positive Solution branch for elliptic problems with critical indefinite nonlinearity, Diff. Integ Equns, 18, No.7, 2005, 721-764. 
  10. (with Dharmatti Sheetal) Zero Sum Differential games involving Hybrid Controls , Jl. Optimization, Theor. Appl., Vol 128, No. 1, 2006, 75-102. 
  11. (with R.Shivaji) Multiple Positive solutions for classes of p− Laplacian equations, Diff. Integ Equns. 17, no.11-12,2004 1255-1261. 
  12. (with G. Barles) Sufficient structure conditions for uniqueness of fully nonlinear equations. Nonlinear Diff. Equns and Applications, 12 , 2005, 503-523. 
  13. (with Andreas Unterreiter) Generalized Hardy-Sobolev inequalities and exponential decay of the Entropy of g(x)∂u/∂t = ∆u. Monatsheft fur Mathematik , 143,No.1, (2004) 35-59. 
  14. (with J.Giacomoni and L. Marcello) Some elliptic indefinite problems on RN, Proc. Royal Soc. Ed. A,134 (2004) No.2,333-361. 
  15. (with P.L.Sachdev and Srinivasa Rao) Self similar solutions of a generalized Burger’s equation with nonlinear damping, Nonlinear Anal,Real World Appl. 4 (2003) No. 5, 723-741. 
  16. (with J.Prajapat) Apriori estimates for solutions of subcritical problems on CR sphere, Advanced Nonlinear Studies, 3, no. 3 (2003) 355–396. 
  17. (with L.Damascelli and F.Pacella) A Strong Maximum Principle for a class of nonpositone singular elliptic problems, Nonlinear Differential Equations and Applications, 10 (2003), 187-196. 
  18. (with J. Dolbeault and M.J. Esteban) Radial Singular Solutions of a critical Problem in a ball, Diff and Integ. Equns. 15 (2002), no. 12, 1459–1474. 
  19. (with P.L.Sachdev and Srinivasa Rao) Analysis of the self similar solutions of the nonplanar Burger’s equation, Nonlinear Analysis, T, M & A. 51 (2002), no. 8, 1447– 1472. 
  20. (with Adimurthi and N.Chaudhuri) An Improved Hardy-Sobolev inequality and its application, Proc. Amer. Math. Soc., 130 (2002), no. 2, 489–505. 
  21. (with N.Chaudhuri) Existence of Positive Solutions of Some Semilinear Elliptic Equations with Singular Coefficients, Proc. Royal Soc. Ed. 131 (2001), no. 6, 1275-1295. 
  22. (with P.L.Sachdev and Srinivasa Rao) Analysis of the self similar solutions of a generalized Burger’s equation with nonlinear damping, Mathematical Problems in engineering, 7 (2001), 253-282. 
  23. (with L.Damascelli) Symmetry of C1 solutions of p-Laplace Equations in RN , Advanced Nonlinear Studies, vol. 1, no. 1 (2001) 40–64. 

Prior to 2000

  1. (with L.Damascelli and F.Pacella) Symmetry of Ground States of p-Laplace Equations via the Moving Plane Method, Arch. Ratl. Mech. Anal. 148 (1999) pp 291-308. 
  2. (with B.Brighi) On some general semilinear elliptic problems with nonlinear boundary conditions, Adv. Differential Equations 4 (1999), no. 3, 369–390. 
  3. (with M.Chipot) Semilinear elliptic problems with nonlinear boundary conditions, Diff Equns and Dyn. Systems , Vol 6 (1,2) , (1998) pp 51-75. 
  4. (with F. Pacella, M. Grossi and S. Kesavan) Symmetry results for the positive solutions of the p-Laplacian, Topological Methods in Nonlinear Analysis, vol. 12, (1998), pp 47- 59. 
  5. (with S. Ramaswamy) Local property of viscosity solutions of fully nonlinear second order elliptic partial differential equations, Bol.Soc.Mat.Mexicana (3) Vol.2, 1996, pp 31-40. 
  6. (with H. Ishii) Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients, Comm.P.D.E., Vol 20, No.11 & 12 (1995), pp. 2187-2213. 
  7. (with M.J. Esteban) Nonexistence result for positive solutions of nonlinear elliptic degenerate problems, Nonlinear Analysis T.M.A. Vol 26, No. 4 (1996) pp 835- 843. 
  8. (with S. Ramaswamy) Maximum Principle for viscosity subsolutions of some second order linear operators and some consequences, Nonlinear Analysis T.M.A. Vol 26, No. 3(1996) pp 415.428. 
  9. (with S. Ramaswamy) Perron’s method and barrier functions for the Dirichlet problem for the viscosity solutions of some nonlinear pde’s. Zeitchrift fur Analysis und Ihre Anqwndungen 13(1994) 2, pp. 199 - 207. 
  10. (with H.B. Keller) A local study at a double critical point for the Taylor - Couette flow, Acta Mechanica, 109 (1995) 27 - 39. 
  11. (with H.B. Keller) The calculation of the coefficients in the reduced bifurcation equation for the Taylor problem. Eur. J. Mechanics, B/Fluids, 10, No. 2 - Suppl., pp. 316, 1991. 
  12. A counterexample to a conjecture of Saint Venant, Vol. 27, 1992, JL. Elasticity, pp. 183-192.44. 
  13. On a counterexample to a conjecture of Saint Venant, Nonlinear Analysis T.M.A., Vol.15, No. 9, 1990, pp. 891-894. 
  14. A counterexample to a conjecture of Saint Venant via reflection methods, Diff. Integ. Equa., Vol. 3, No. 4, 1990, pp. 653-662. 
  15. (with P.N. Srikanth) Multiplicity results for an ODE via Morse index calculations, Houston J. Math., Vol. 15, No. 4, 1989. 
  16. (with P.N. Srikanth) Symmetry breaking for a class of semilinear elliptic problems, Trans. Amer. Math. Soc., Vol. 304, No.2, December 1987, pp. 839 - 845. 
  17. On the global set of solutions of a nonlinear O.D.E. : Theoretical and Numerical description, J.D.E., Vol. 65, No. 1, October 1986, pp. 1-48. 
  18. Comportement global des solutions d’une equation nonlineaire, C.R. Acad. Sc. PARIS, t.298, Serie I, No. 14, 1984, pp. 325-328. 
  19. (with Daniela Giachetti) Existence and homogenization for semi linear elliptic equa- tions with non compact nonlinearity, Nonlinear Analysis T.M.A., Vol. 8, No. 1, 1984, pp. 5-15. 
  20. On a nonlinear elliptic equation with periodic coefficients, SIAM J. Appl. Math., Vol. 40, No. 3, June 1981, pp. 409 - 418. 

IN BOOKS/ BOOK CHAPTERS 

  1. (with F. Pacella ) Symmetry of solutions of elliptic equations via maximum principles, Handbook of differential equations: stationary partial differential equations. Vol. VI, 269–312, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2008. 
  2. (with Giacomoni, Jacques;  Prajapat, Jyotshana. ) Positive solution branch for elliptic problems with critical indefinite nonlinearity. Recent advances in elliptic and parabolic problems, 81–95, World Sci. Publ., Hackensack, NJ, 2005.

LECTURE NOTES 

  1. Partial Differential Equations, by F. John (Notes by Mythily Ramaswamy and N. Shivaramakrishnan) An expanded version was published by Springer Verlag in 1979. 
  2. On numerical methods in bifurcation problems, by H.B. Keller (Notes by Mythily Ramaswamy and A.K. Nandakumaran) T.I.F.R. Lecture Notes No. 79 (1987)

 


POPULAR SCIENCE ARTICLES 

  1. Sonya Kovalevskaya, The First Woman Mathematician of Modern Times, Resonance, Vol 1, No. 9, 1996. 
  2. Emmy Noether, Resonance, Vol 3, No. 9, 1998.