scholarly journals Global Existence of Weak Solutions to a Fractional Model in Magnetoelastic Interactions

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Idriss Ellahiani ◽  
EL-Hassan Essoufi ◽  
Mouhcine Tilioua
Keyword(s):  
Mathematical Model ◽  
Global Existence ◽  
Evolution Equation ◽  
Weak Solutions ◽  
Penalty Method ◽  
Fractional Model ◽  
Existence Of Weak Solutions ◽  
Commutator Estimates ◽  
One Dimensional ◽  
Magnetization Field

The paper deals with global existence of weak solutions to a one-dimensional mathematical model describing magnetoelastic interactions. The model is described by a fractional Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We prove global existence by using Faedo-Galerkin/penalty method. Some commutator estimates are used to prove the convergence of nonlinear terms.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

scholarly journals Global existence of weak solutions for Landau-Lifshitz-Maxwell equations

2007 ◽  
Vol 17 (4) ◽  
pp. 867-890 ◽  
Author(s):  
Shijin Ding ◽  
◽  
Boling Guo ◽  
Junyu Lin ◽  
Ming Zeng ◽  
...  
Keyword(s):  
Global Existence ◽  
Weak Solutions ◽  
Maxwell Equations ◽  
Existence Of Weak Solutions
Sign in / Sign up

Export Citation Format

Share Document