Advanced Level Training Programme 2014


    Distribution Theory; Sobolev Spaces; Elliptic PDE: weak solution, Lax-Milgram Lemma, regularity results, weak maximum principle, eigenvalue problems; Heat and Wave Equations: existence, uniqueness etc; Semigroup theory; First Order Hyperbolic PDEs; Existence of weak solution, entropy solution; Finite Difference/Finite Volume Schemes for First Order Equations; Finite Element Methods for Elliptic and Heat Equations; Review of Finite Dimensional Control Theory; Controllability and Observability; Stability and Stabilizability; Control Theory for linear second order PDEs, Optimal Control for Elliptic & Heat Equations with FEM Computations