Methods for partial differential equations qualitative properties of solutions, phase space analysis, semilinear models - Ebert, Marcelo R.; Reissig, Michael (Cham, Switzerland Birkhauser, 2018)
Part 1 -- Introduction -- Part 2 -- Partial differential equations in models -- Basics for partial differential equations -- The Cauchy-Kovalevskaja theorem -- Holmgren's uniqueness theorem -- Method of characteristics -- Burger's equation -- Laplace equation -- properties of solutions -- starting point of elliptic theory -- Heat equation -- properties of solutions -- starting point of parabolic theory -- Wave equation -- properties of solutions -- starting point of hyperbolic theory -- Energies of solutions -- one of the most important quantities -- Part 3 -- Phase space analysis for heat equation -- Phase space analysis and smoothing for Schrèodinger equations -- Phase space analysis for wave models -- Phase space analysis for plate models -- The method of stationary phase and applications -- Part 4 -- Semilinear heat models -- Semilinear classical damped wave models -- Semilinear wave models with a special structural dissipation -- Semilinear classical wave models -- Semilinear Schrèodinger models -- Linear hyperbolic systems -- Part 5 -- Research projects for beginners -- Background material.
Keywords: Differential equations, Partial