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A coupled system of fractional order integral equations in reflexive Banach spaces

100%
El-Sayed A. M. A., Hashem H. H. G.
Commentationes Mathematicae
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2012
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tom 52
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nr 1
EN
We present an existence theorem for at least one weak solution for a coupled system of integral equations of fractional order in reflexive Banach spaces relative to the weak topology.
2
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On weak-strong uniqueness property for full compressible magnetohydrodynamics flows

100%
Yan W.
Open Mathematics
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2013
|
tom 11
|
nr 11
2005-2019
EN
This paper is devoted to the study of the weak-strong uniqueness property for full compressible magnetohydrodynamics flows. The governing equations for magnetohydrodynamic flows are expressed by the full Navier-Stokes system for compressible fluids enhanced by forces due to the presence of the magnetic field as well as the gravity and an additional equation which describes the evolution of the magnetic field. Using the relative entropy inequality, we prove that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists.
3
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Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients

88%
Li H., Ji S.
Open Mathematics
|
2011
|
tom 9
|
nr 2
269-280
EN
This paper is concerned with an optimal control problem governed by the nonlinear one dimensional periodic wave equation with x-dependent coefficients. The control of the system is realized via the outer function of the state. Such a model arises from the propagation of seismic waves in a nonisotropic medium. By investigating some important properties of the linear operator associated with the state equation, we obtain the existence and regularity of the weak solution to the state equation. Furthermore, the existence of the optimal control is proved by means of the Arzelà-Ascoli lemma and Sobolev compact imbedding theorem.
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