Long-Time Existence for Semi-Linear Klein–Gordon Equations with Quadratic Potential
نویسندگان
چکیده
منابع مشابه
Long-time existence for semi-linear Klein-Gordon equations with quadratic potential
We prove that small smooth solutions of semi-linear Klein-Gordon equations with quadratic potential exist over a longer interval than the one given by local existence theory, for almost every value of mass. We use normal form for the Sobolev energy. The difficulty in comparison with some similar results on the sphere comes from the fact that two successive eigenvalues λ, λ′ of √ −∆+ |x|2 may be...
متن کاملHaar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems
In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, Haar wavelets are applied for converting the TBVP, as a system of differential equations, in to a system of matrix algebraic equations...
متن کاملGlobal Existence Results for Nonlinear Schrödinger Equations with Quadratic Potentials
We prove that no finite time blow up can occur for nonlinear Schrödinger equations with quadratic potentials, provided that the potential has a sufficiently strong repulsive component. This is not obvious in general, since the energy associated to the linear equation is not positive. The proof relies essentially on two arguments: global in time Strichartz estimates, and a refined analysis of th...
متن کاملLONG-TIME EXISTENCE FOR SEMI-LINEAR KLEIN-GORDON EQUATIONS WITH SMALL CAUCHY DATA ON ZOLL MANIFOLDS By J.-M. DELORT and J. SZEFTEL
We prove a long time existence result for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds. This generalizes a preceding result concerning the case of spheres, obtained in an earlier paper by the authors. The proof relies on almost orthogonality properties of products of eigenfunctions of positive elliptic selfadjoint operators on a compact manifold and on the specifi...
متن کاملSemi-linear wave equations
This survey reviews some of the recent work on semilinear wave equations, in particular the wave map equation. We discuss wellposedness, as well as the construction of special solutions and their stability. Mathematics Subject Classification (2010). 35L05, 35L52, 37K40, 37K45, 53Z05
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2010
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300903509112