scholarly journals A generalization of the Lions-Temam compact imbedding theorem

1990 ◽  
Vol 115 (4) ◽  
pp. 338-342 ◽  
Author(s):  
Tomáš Roubíček
Keyword(s):  
Compact Imbedding

scholarly journals Compact Imbedding Theorems with Symmetry of Strauss–Lions Type for the Space W1,()(Ω)

2001 ◽  
Vol 255 (1) ◽  
pp. 333-348 ◽  
Author(s):  
Xianling Fan ◽  
Yuanzhang Zhao ◽  
Dun Zhao
Keyword(s):  
Compact Imbedding

A compact imbedding

1984 ◽  
pp. 63-78
Author(s):  
Henrik Schlichtkrull
Keyword(s):  
Compact Imbedding

A Compact Imbedding Theorem for Functions without Compact Support

1971 ◽  
Vol 14 (3) ◽  
pp. 305-309 ◽  
Author(s):  
R. A. Adams ◽  
John Fournier
Keyword(s):  
Sobolev Space ◽  
Compact Support ◽  
Unbounded Domains ◽  
Bounded Domains ◽  
Complete Continuity ◽  
Compact Imbedding ◽  
Compactness Theorems ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Made In

The extension of the Rellich-Kondrachov theorem on the complete continuity of Sobolev space imbeddings of the sort1to unbounded domains G has recently been under study [1–5] and this study has yielded [4] a condition on G which is necessary and sufficient for the compactness of (1). Similar compactness theorems for the imbeddings2are well known for bounded domains G with suitably regular boundaries, and the question naturally arises whether any extensions to unbounded domains can be made in this case.

Existence of Minimizer to the Ginzburg-Landau Free Energy of Ferromagnetic System

2013 ◽  
Vol 444-445 ◽  
pp. 717-722
Author(s):  
Li Mei Li ◽  
Hong Luo
Keyword(s):  
Free Energy ◽  
Sobolev Space ◽  
Monotone Operator ◽  
Ginzburg Landau ◽  
Landau Free Energy ◽  
Lower Semi ◽  
Ferromagnetic System ◽  
Compact Imbedding

In this paper, we obtain the existence of minimizer to Ginzburg-Landau free energy of ferromagnetic system by coercivity and weakly lower semi-continuity of the free energy, where the weakly lower semi-continuity is derived from monotone operator condition and the Sobolev space compact imbedding theorem.

A compact imbedding result on Lipschitz manifolds

1991 ◽  
Vol 290 (1) ◽  
pp. 491-508 ◽  
Author(s):  
Kevin McLeod ◽  
Rainer Picard
Keyword(s):  
Compact Imbedding

scholarly journals Uniform Attractor and Approximate Inertial Manifolds for Nonautonomous Long-Short Wave Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-17
Author(s):  
Hongyong Cui ◽  
Jie Xin
Keyword(s):  
Phase Space ◽  
Initial Data ◽  
Wave Equations ◽  
Short Wave ◽  
Inertial Manifolds ◽  
Inertial Manifold ◽  
Uniform Attractor ◽  
Approximate Inertial Manifolds ◽  
Compact Imbedding ◽  
Space Method

Nonautonomous long-short wave equations with quasiperiodic forces are studied. We prove the existence of the uniform attractor for the system by means of energy method, which is widely used to deal with problems who have no continuity (with respect to the initial data) property, as well as to those which Sobolev compact imbedding cannot be applied. Afterwards, we construct an approximate inertial manifold by means of extending phase space method and we estimated the size of the corresponding attracting neighborhood for this manifold.

scholarly journals On a Nonlinear Wave Equation Associated with Dirichlet Conditions: Solvability and Asymptotic Expansion of Solutions in Many Small Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-33 ◽  
Author(s):  
Le Thi Phuong Ngoc ◽  
Le Khanh Luan ◽  
Tran Minh Thuyet ◽  
Nguyen Thanh Long
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Weak Solution ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Taylor Expansion ◽  
The Other ◽  
Small Parameters ◽  
Compact Imbedding ◽  
Asymptotic Expansion Of Solutions

A Dirichlet problem for a nonlinear wave equation is investigated. Under suitable assumptions, we prove the solvability and the uniqueness of a weak solution of the above problem. On the other hand, a high-order asymptotic expansion of a weak solution in many small parameters is studied. Our approach is based on the Faedo-Galerkin method, the compact imbedding theorems, and the Taylor expansion of a function.

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