Among nonlinear PDEs, dispersive and wave equations form an important class of
equations. These include the nonlinear Schrodinger equation, the nonlinear wave equation …

This book presents in a self-contained form the typical basic properties of solutions to
semilinear evolutionary partial differential equations, with special emphasis on global …

These notes are based on a course I gave at UCLA in the fall of 1994. I tried to make the
course self-contained, presenting as background basic facts about the solution of the linear …

We study the scattering theory of a conservative nonlinear one-parameter group of operators
on a Hilbert space X relative to a group of linear unitary operators. Under certain …

1. Introduction. The main goal of this paper is to prove" Sobolev inequali-ties" for constant
coefficient second order differential operators with bounds which do not depend on the …

4x3 0)= f (x),%(X, 0)= g (x)(1) with f, g E CF (lR'). It is well known that this problem does not
admit a global solution (ie, one defined for all (x, t) E IR” x [0, co)) for any p> 1 when the …

This book provides an overview of different topics related to the theory of partial differential
equations. Selected exercises are included at the end of each chapter to prepare readers for …

In this paper we study the Cauchy problem to the linear damped wave equation utt Ą Du ž
2aut ¼ 0 in š0, yŽ Ā Rn šn b 2Ž. It has been asserted that the above equation has the …

A simple two-fluid model to describe the dynamics of a plasma is the Euler–Poisson system,
where the compressible electron fluid interacts with its own electric field against a constant …

Global Existence of Small Solutions to Nonlinear Evolution Equations Page 1 JOURNAL OF
DIFFERENTIAL EQUATIONS 46, 409-425 (1982) Global Existence of Small Solutions to …