scholarly journals A Two-Dimensional Landau-Lifshitz Model in Studying Thin Film Micromagnetics

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
Jingna Li
Keyword(s):  
Thin Film ◽  
Weak Solution ◽  
Semigroup Theory ◽  
Higher Order ◽  
Order Equation ◽  
Two Dimensional ◽  
Lifshitz Equation ◽  
Local Weak Solution ◽  
Penalty Approximation ◽  
Higher Order Equation

The paper is concerned with a two-dimensional Landau-Lifshitz equation which was first raised by A. DeSimone and F. Otto, and so fourth, when studying thin film micromagnetics. We get the existence of a local weak solution by approximating it with a higher-order equation. Penalty approximation and semigroup theory are employed to deal with the higher-order equation.

scholarly journals A Liouville theorem for the higher-order fractional Laplacian

2019 ◽  
Vol 21 (02) ◽  
pp. 1850005 ◽  
Author(s):  
Ran Zhuo ◽  
Yan Li
Keyword(s):  
Positive Solutions ◽  
Fractional Laplacian ◽  
Liouville Theorem ◽  
Integral Form ◽  
Higher Order ◽  
Order Equation ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Higher Order Equation ◽  
Fractional Equation

We study Navier problems involving the higher-order fractional Laplacians. We first obtain nonexistence of positive solutions, known as the Liouville-type theorems, in the upper half-space [Formula: see text] by studying an equivalent integral form of the fractional equation. Then we show symmetry for positive solutions on [Formula: see text] through a delicate iteration between lower-order differential/pseudo-differential equations split from the higher-order equation.

On the Decomposition of Spinor Fields which satisfy a Nonlinear Higher Order Equation

1983 ◽  
Vol 38 (12) ◽  
pp. 1293-1295
Author(s):  
D. Großer
Keyword(s):  
Field Theory ◽  
Higher Order ◽  
Order Equation ◽  
Field Theories ◽  
First Order ◽  
Spinor Fields ◽  
Fermion Fields ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
Higher Order Equation

Abstract A field theory which is based entirely on fermion fields is non-renormalizable if the kinetic energy contains only derivatives of first order and therefore higher derivatives have to be included. Such field theories may be useful for describing preons and their interaction. In this note we show that a spinor field which satisfies a higher order field equation with an arbitrary nonlinear selfinteraction can be written as a sum of fields which satisfy first order equations.

Sign in / Sign up

Export Citation Format

Share Document