# 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)