Global strong solution to a nonlinear Dirac type equation in one dimension
نویسندگان
چکیده
منابع مشابه
Global Strong Solution to a Nonlinear Dispersive Wave Equation
In this paper, compared with the previous results, a new global existence for strong solutions to the equation is acquired provided that the potential (1−∂2 x)u0 changes sign on R, which improves considerably the previous result. Mathematics Subject Classification: 35G25, 35L05, 35Q35
متن کاملGlobal Solution for the Nonlinear Beam Equation
We prove the existence and uniqueness of global solution for the nonlinear beam equation with initial boundary condition: Q in x f u g t u u M u u ) ( ) ( ) ( ) ( 2 2 2 = ′ + Δ ∇ − Δ + ′ ′ φ α where tt u t x u = ′ ′ ) , ( , t u t x u = ′ ) , ( , 0 > α , φ , , g M is nonlinear functions and Δ is Laplacian in n R .
متن کاملOn a Nonlinear Dirac Equation of Yamabe Type
We show a conformal spectral estimate for the Dirac operator on a non-conformally-flat Riemannian spin manifolds of dimension n ≥ 7. The estimate is a spinorial analogue to an estimate by Aubin which solved the Yamabe problem for the above manifolds. Using Hijazi’s inequality our estimate implies Aubin’s estimate. More exactly, let M be a compact manifold of dimension n ≥ 7 equipped with a Riem...
متن کاملOne Component Dirac Equation
We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac equation, exist. A partial set of translations between complex and complexified quaternionic quantum mechanics may be defined. a) e-mail address: [email protected]
متن کاملGlobal Bounds for the Cubic Nonlinear Schrödinger Equation (nls) in One Space Dimension
This article is concerned with the small data problem for the cubic nonlinear Schrödinger equation (NLS) in one space dimension, and short range modifications of it. We provide a new, simpler approach in order to prove that global solutions exist for data which is small in H. In the same setting we also discuss the related problems of obtaining a modified scattering expansion for the solution, ...
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: Nonlinear Analysis: Theory, Methods & Applications
سال: 2013
ISSN: 0362-546X
DOI: 10.1016/j.na.2012.10.008