Linear Partial Differential Equations -- Nonlinear Model Equations and Variational Principles -- First-Order, Quasi-Linear Equations and Method of Characteristics -- First-Order Nonlinear Equations and Their Applications -- Conservation Laws and Shock Waves -- Kinematic Waves and Real-World Nonlinear Problems -- Nonlinear Dispersive Waves and Whitham’s Equations -- Nonlinear Diffusion-Reactio…
Mathematical Methods -- Passive Scalar Diffusion as a Damped Wave -- Extremalizing Vector Fields as Guides Toward Understanding Properties of Turbulence -- Low-Wavenumber Forcing and Turbulent Energy Dissipation -- New Potential Symmetries for a Generalised Inhomogeneus Nonlinear Diffusion Equation -- DNS and New Scaling Laws of ZPG Turbulent Boundary Layer Flow -- Linear Instability of a Slowl…
I Preliminaries -- II Semimartingales and Stochastic Integrals -- III Semimartingales and Decomposable Processes -- IV General Stochastic Integration and Local Times -- V Stochastic Differential Equations -- VI Expansion of Filtrations -- References.It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many…
Nonnegative Markov Chains with Applications -- Phase Changes with Time and Multi-Scale Homogenizations of a Class of Anomalous Diffusions -- Semi-Markov Cascade Representations of Local Solutions to 3-D Incompressible Navier-Stokes -- Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures -- Enstrophy and Ergodicity Of Gravity Currents -- Stochastic Heat and Burgers …