A Dynamical Systems Approach to Theory and Practice
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincare's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our ......
This paper is a corrigendum and improvements to Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations and its consequences. We give here the corrected proofs of the concerned results, improving most of them.
We consider the combined power-type nonlinear Schr?odinger equations with energy-critical growth, and study the solutions slightly above the ground state threshold at low frequencies, so that we obtain a so-called nine-set theory developed by Nakanishi and Schlag [24, 25].
We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R3: ?ttu ? ?u +m j=1 Vj (x ? vj t) u = 0. The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the ......
In this paper, we establish a necessary and sufficient condition for the existence and regularity of the density of the solution to a semilinear stochastic (fractional) heat equation with measure-valued initial conditions. Under a mild cone condition for the diffusion coefficient, we establish the smooth joint density at multiple points. The tool ......
A Dynamical Systems Approach to Theory and Practice
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincare's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our ......
This book gives an extensive survey of many important topics in the theory of Hamilton-Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly, the basic well-posedness theory of viscosity solutions for first-order Hamilton-Jacobi equations is covered. Then, the homogenization theory, a very active research topic ......
This text introduces students to the theory and practice of differential equations, which are fundamental to the mathematical formulation of problems in physics, chemistry, biology, economics, and other sciences. The book is ideally suited for undergraduate or beginning graduate students in mathematics, and will also be useful for students in the ......
