Publications



  • Scalar Conservation laws with discontinuous flux, M.S.thesis, Indian Institute of Science, March 2003. (.pdf)

  • Convergence of upwind difference schemes for a scalar conservation law with indefinite discontinuities in the flux function, SIAM Journal on Numerial Analysis, 43 (2), 2005, 559 - 577. (.pdf)

  • On Conservation laws with discontinuous flux, with R.Buerger, K.H.Karlsen and J.D.Towers,In: Y. Wang and K. Hutter (Eds.), Trends in Applications of Mathematics to Mechanics , Shaker Verlag, Aachen, 75-84 (2005).(.pdf)

  • Image processing using topological optimization, with A.Ahmeed et al, Proc. of Workshop on Modelling in Life, Material Sciences and Technology, ICTP, Trieste, 2005.(.pdf)

  • Optimal entropy solutions for conservation laws with discontinuous flux functions, with Adimurthi and G.D.Veerappa Gowda, Journal of Hyperbolic Differential Equations, 2 (4), 2005, 783 - 837. (.pdf)

  • Conservation laws with flux function discontinuous in the space variable - II, Convex-Concave type fluxes and Generalised entropy solutions, with Adimurthi and G.D.Veerappa Gowda, Preprint, 2004, To appear in Journal of Computational and Applied Math (.pdf)

  • Analysis and Numerical Approximation of Conservation laws with discontinuous coefficients, PhD thesis, Indian Institute of Science, March 2005. (.pdf)

  • On the upstream mobility flux scheme for two phase flow in porous medium with changing rock types, with Jerome Jaffre, Preprint, 2005. ,(.pdf)

  • Convergence of Godunov type schemes for a conservation law with spatially varying discontinuous flux function, with Adimurthi and G.D.Veerappa Gowda, Preprint, 2005., To appear in Mathematics of Computation (.pdf)

  • Explicit Hopf-Lax type formulas for Hamilton-Jacobi equations and Conservation laws with discontinuous coefficients,with Adimurthi and G.D.Veerappa Gowda, Preprint, 2005.(.pdf)

  • Existence and Stability of entropy solutions for Conservation laws with non-convex discontinuous flux functions, with Adimurthi and G.D.Veerappa Gowda, Preprint, 2006, To appear in Networks and Heterogenous media. (.pdf)

  • Convergence of Finite volume schemes for triangular systems of conservation laws, with Kenneth H. Karlsen and Nils Henrik Risebro, Preprint, 2006. (.pdf)

  • A new class of well-balanced finite volume schemes for conservation laws with source terms, with Kenneth H. Karlsen and Nils Henrik Risebro, Preprint, 2006, (.pdf)

  • Semi-Godunov schemes for general triangular systems of conservation laws, Wwith Kenneth H.Karlsen and Nils Henrik Risebro, Preprint, 2006, (.pdf)

  • A large time-stepping scheme for balance laws, with Kenneth H. Karlsen and Nils Henrik Risebro, Preprint, 2006, (.pdf)

  • Maximal entropy solutions for scalar conservation laws with discontinuous flux, Preprint 2006, (.pdf)






    Talks and Presentations



  • Analysis and Numerical Approximation of Conservation laws with Discontinuous Coefficients, Mathematics Colloquium, TIFR center, Bangalore, February 17, 2004,.(.pdf)

  • Image Processing and Topological Optimization, Workshop for Modelling in Life, Materials Science and Technology, Abdus Salam ICTP, Trieste,Italy, March 31, 2004,.(.pdf)

  • Restoration and Segmentation of Images using the Topological gradient, Workshop in Nonlinear PDE, CMA, Oslo, April 28, 2004.(.pdf)

  • Restoration and Segmentation of Images using the Topological gradient, Numerical Analysis Seminar, INRIA, Rocquencourt, May 24, 2004. (.pdf)

  • Conservation laws with spatially varying coefficients, Seminar talk, Department of Aerospace Engineering, IISc, Bangalore, October 21, 2004.(.pdf)

  • Analysis and Numerical Approximation of Conservation laws with Discontinuous Coefficients, Thesis Colloquium, Departmenet of Mathematics,IISc, Bangalore, January 20, 2005,.(.pdf)

  • Godunov type schemes for conservation laws with spatially varying source terms, Intl. Conf. on Numerical Analysis and Scientific Computing, IMI, IISc, Bangalore, July 18 2005, (.pdf)

  • Finite Volume schemes for simulating a petroleum reservoir with heterogenities, AMD Conf. on Advanced Scientific Computing, organised by AMD inc.., Bangalore, July 21 2005, (.pdf)

  • Finite Volume schemes for the equations of Ideal MHD: a review, PDE seminar, CMA, Oslo, November 17, 2005. (.pdf)

  • Entropy stable schemes for systems of conservation laws, Workshop on Computational methods in Astrophysical problems, CMA, Oslo, January 9, 2006. (.pdf)

  • Well Balanced schemes for conservation laws with singular source terms, MAFELAP 2006, June 12 2006, London. (.pdf)

  • Finite volume schemes for equations of MagnetoHydroDynamics, Trends in Mathematics for Applications, June 19 2006, Oslo. (.pdf)

  • Semi-Godunov schemes for a reduced three phase flow model, SIAM Annual Meeting 2006, July 12, 2006, Boston. (.pdf)

  • Semi-Godunov schemes for general triangular systems of conservation laws, Hyperbolic equations, Theory, Numerics and Applications 2006. July 18 2006, Lyon. (.pdf)

  • Well-Balanced finite volumes schemes for conservation laws with source terms, BIT Numerical Mathematics Nordic Numerical Analysis conference, September 1, 2006, Stockholm, (.pdf)

  • Theory and Numerics for conservation laws with discontinuous fluxes, Colloquium, Department of Mathematics, University of Bari, October 18, 2006, Bari, (.pdf)