This book will explain how group theory underpins some of the key features of particle physics. It will examine symmetries and conservation laws in quantum mechanics and relate these to groups of transformations. Group theory provides the language for describing now particles (a…
We consider a system of n conservation laws: [partial derivative/boundary/degree of a polynomial symbol]∂u [over] [partial derivative/boundary/degree of a polynomial symbol]∂t + [partial derivative/boundary/degree of a polynomial symbol]∂f(u) [over] [partial derivative/boundary/…
Introduction -- Preliminaries -- Green's functions for systems with constant coefficients -- Green's function for systems linearized along shock profiles -- Estimates on green's function -- Estimates on crossing of initial layer -- Estimates on truncation error -- Energy type es…
We are interested in the time-asymptotic behavior of solutions to viscous conservation laws. Through the pointwise estimates for the Green's function of the linearized system and the analysis of coupling of nonlinear diffusion waves, we obtain explicit expressions of the time-as…
