Topics and Speakers


Review of Measure Theory:

-- Measurable functions and properties, Weak convergence, Weak-star convergence of functions.

-- Projection of measures, Convergence of measures.

-- Hahn decomposition of measures.

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.