In this paper we prove the existence of uniform global attractors in the strong topology of the phase space for semiflows generated by vanishing viscosity approximations of some class of non-autonomous complex fluids.
We study here Dirichlet boundary value problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principle part and L^1-control in coefficient of the low-order term. As characteristic feature of such problem is a specification of the matrix of anisotropy A=A^{sym}+A^{skew} in BMO-space. Since we cannot expect to have a solution of the state equation in the classical Sobolev space W^{1,p}_0(\Omega), we specify a suitable functional class in which we look for solutions and prove existence of weak solutions in the sense of Minty using a non standard approximation procedure and compactness arguments in variable spaces.
We study an optimal control problem for degenerate elliptic variation inequality with degenerate weight function of potential type in the so-called class of H-admissible solutions. Using an appropriate regular algorithm of perturbation, we prove attainability of H-optimal pairs via optimal solutions of some non-degenerate perturbed optimal control problems.
It is shown that `a free function' in the evolution equation of Hornig & Schindler for the magnetic induction (Physics of Plasmas, 3 (3), 781 - 791) has a unique representation, obtained in an explicit form. Some conclusions of the explicit formulation of the evolution equation are discussed.
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