Classical Bounded Variation (BV) compactness:
-- Vanishing viscosity method.
-- Functions of bounded variations.
-- Time-continuity estimates.
-- BV compactness.
-- Existence, Uniqueness, Continuous dependence estimates.
Numerical aspects of Conservation Laws:
-- Finite difference/volume schemes.
-- Finite element schemes.
-- Consistency and stability of schemes.
-- Convergence of numerical schemes using BV compactness.
Young Measure theory:
-- Measure valued solutions.
-- Process solutions.
-- Young measure and basic properties.
-- Nonlinear Weak-star convergence.
-- Application to scalar conservations laws in multi-dimensions.
Compensated Compactness theory in one dimension:
-- Div-Curl Lemma.
-- Murat's Lemma.
-- Compensated Compactness theorem.
-- Application to scalar conservation laws.
Compensated Compactness theory in multi-dimensions:
-- Measure valued solutions.
-- H-measures and basic properties.
-- Localization principle and strong pre-compactness.
-- Application to scalar conservation laws.
Kinetic theory and its application to Conservation Laws:
-- Kinetic formulation.
-- Entropy defect measures, Gibbs principle.
-- Compactness and kinetic averaging lemmas.
-- Application to scalar conservation laws.
Tentative List of Speakers
-- Prof. Adi Adimurthi (TIFR CAM).
-- Dr. Imran Habib Biswas (TIFR CAM).
-- Dr. Praveen Chandrashekar (TIFR CAM).
-- Dr. Rajib Dutta (IISER Kolkata).
-- Prof. G. D. Veerappa Gowda (TIFR CAM).
-- Prof. K. T. Joseph (TIFR CAM).
-- Prof. Sandeep K. (TIFR CAM).
-- Dr. Ujjwal Koley (TIFR CAM).
-- Prof. M. Vanninathan (TIFR CAM).
--Partial Differential Equations by L.C. Evans.
--Hyperbolic System of Conservation Laws by Godlewski & Raviart,Vol I & II.
--Numerical Methods for Conservation Laws by R. J. Leveque.
--Shock Waves and Reaction Diffusion Equations by J. Smoller.
--Weak and Measure Valued Solutions to Evolutionary PDEs by J. Málek et al.
--Kinetic Formulation of Conservation Laws by B. Perthame.
