HCDTE Lecture Notes. Part I. Nonlinear Hyperbolic PDEs, Dispersive and Transport Equations

This is the first of two volumes containing the lecture notes of some of the courses given during the intensive trimester HCDTE, Nonlinear Hyperbolic PDEs, Dispersive and Transport Equations: analysis and control, held at SISSA, Trieste (Italy) from May 16th to July 22nd, 2011. The lectures covered a number of different topics within the fields of hyperbolic equations, fluid dynamic, dispersive and transport equations, measure theory and control and they were primarily intended for PhD students and young researchers at the beginning of their career. 1. I. Chueshov and I. Lasiecka, Well-posedness and long time behavior in nonlinear dissipative hyperbolic-like evolutions with critical exponents. 2. J.-F. Coulombel, Stability of finite difference schemes for hyperbolic initial boundary value problems. 3. S. Liu and R. Triggiani, Boundary control and boundary inverse theory for non-homogeneous second order hyperbolic equations: a common Carleman estimates approach.