Semilinear Wave Equations

نویسنده

  • MICHAEL STRUWE
چکیده

We survey existence and regularity results for semi-linear wave equations. In particular, we review the recent regularity results for the u5-Klein Gordon equation by Grillakis and this author and give a self-contained, slightly simplified proof.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Shooting Methods for Numerical Solutions of Exact Controllability Problems Constrained by Linear and Semilinear 2-d Wave Equations

Abstract. Numerical solutions of exact controllability problems for linear and semilinear 2-d wave equations with distributed controls are studied. Exact controllability problems can be solved by the corresponding optimal control problems. The optimal control problem is reformulated as a system of equations (an optimality system) that consists of an initial value problem for the underlying (lin...

متن کامل

Existence of Global Solutions to Supercritical Semilinear Wave Equations

In this work we study the existence of global solution to the semilinear wave equation (∂

متن کامل

Rotationally Invariant Periodic Solutions of Semilinear Wave Equations

Under suitable conditions we are able to solve the semilinear wave equation in any dimension. We are also able to compute the essential spectrum of the linear wave operator for the rotationally invariant periodic case.

متن کامل

Stability and convergence of staggered Runge-Kutta schemes for semilinear wave equations

A staggered Runge-Kutta (staggered RK) scheme is the time integration Runge-Kutta type scheme based on staggered grid, which was proposed by Ghrist and Fornberg and Driscoll in 2000. Afterwords, Vewer presented efficiency of the scheme for linear and semilinear wave equations through numerical experiments. We study stability and convergence properties of this scheme for semilinear wave equation...

متن کامل

Almost Global Existence for Some Semilinear Wave Equations with Almost Critical Regularity

For any subcritical index of regularity s > 3/2, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the initial data are small in the Sobolev space Hs × Hs−1 with certain angular regularity. The main new ingredient in the proof is an endpoint version of the generalized Strichartz estimates in the space Lt...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008