ON THE ZERO THICKNESS LIMIT OF THIN FERROMAGNETIC FILMS WITH SURFACE ANISOTROPY ENERGY

2001 ◽  
Vol 11 (08) ◽  
pp. 1469-1490 ◽  
Author(s):  
K. HAMDACHE ◽  
M. TILIOUA
Keyword(s):  
Maxwell Equations ◽  
Existence Of Solutions ◽  
Anisotropy Energy ◽  
Surface Anisotropy ◽  
Magnetic Polarization ◽  
One Dimensional ◽  
Ferromagnetic Films ◽  
Lifshitz Equation ◽  
Global Existence Of Solutions ◽  
Model Equations

We discuss the behaviour, when the thickness ε tends to 0, of thin ferromagnetic films with surface anisotropy energy. The model equations are given by the Landau–Lifshitz equation coupled to Maxwell equations with magnetic polarization. We consider two types of materials: flat and slender cylinders. Two scalings for the surface anisotropy coefficient are used. In the first one it is assumed that the coefficient is of order ε while in the second one we suppose that it is of order 1. We prove global existence of solutions and show that the zero-thickness limit induces new effects. For example, for slender media we get a nonlocal effect for the magnetic excitation while for flat media we obtain a one-dimensional magnetic field.

scholarly journals Exponential decay and global existence of solutions of a singular nonlocal viscoelastic system with distributed delay and damping terms

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 795-826
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras ◽  
Djamel Ouchenane
Keyword(s):  
Exponential Decay ◽  
Source Term ◽  
Existence Of Solutions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Distributed Delay ◽  
Viscoelastic System ◽  
Nonlinear Source ◽  
One Dimensional ◽  
Global Existence Of Solutions

We investigate in this work a singular one-dimensional viscoelastic system with a nonlinear source term, distributed delay, nonlocal boundary condition, and damping terms. By the theory of potentialwell, the existence of a global solution is established, and by the energy method and the functional of Lyapunov, we prove the exponential decay result. This work is an extension of Boulaaras? work in ([3] and [27]).

Global existence, asymptotic behavior and uniform attractor for a non-autonomous Timoshenko system of type III with weak damping

2020 ◽  
pp. 1-25
Author(s):  
Yuming Qin ◽  
Ye Sheng
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Uniform Attractor ◽  
Timoshenko System ◽  
One Dimensional ◽  
Type Iii ◽  
Global Existence Of Solutions ◽  
Decay Of Solutions ◽  
Weak Damping

In this paper, we investigate one-dimensional thermoelastic system of Timoshenko type III with double memory dampings. At first we give the global existence of solutions by using semigroup theory. Then we can prove the energy decay of solutions by constructing a series of Lyapunov functionals and obtain the existence of absorbing ball. Finally, we prove the asymptotic compactness by using uniform contractive functions and obtain the existence of uniform attractor.

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 The Muskat problem with surface tension and equal viscosities in subcritical $$L_p$$-Sobolev spaces

2021 ◽  
Author(s):  
Anca-Voichita Matioc ◽  
Bogdan-Vasile Matioc
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Well Posedness ◽  
Global Existence Of Solutions ◽  
Muskat Problem ◽  
The Mathematical Model ◽  
Quasilinear Parabolic

AbstractIn this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $$W^s_p(\mathbb {R})$$ W p s ( R ) , where $${p\in (1,2]}$$ p ∈ ( 1 , 2 ] and $${s\in (1+1/p,2)}$$ s ∈ ( 1 + 1 / p , 2 ) . This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $$W^{\overline{s}-2}_p(\mathbb {R})$$ W p s ¯ - 2 ( R ) , where $${\overline{s}\in (1+1/p,s)}$$ s ¯ ∈ ( 1 + 1 / p , s ) . Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions.

scholarly journals One-dimensional in-plane edge domain walls in ultrathin ferromagnetic films

Nonlinearity ◽  
2018 ◽  
Vol 31 (3) ◽  
pp. 728-754 ◽  
Author(s):  
Ross G Lund ◽  
Cyrill B Muratov ◽  
Valeriy V Slastikov
Keyword(s):  
Domain Walls ◽  
One Dimensional ◽  
Ferromagnetic Films
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