In this paper, we first establish a criterion based on contractive function for the existence of generalized polynomial attractors. This only involves some rather weak compactness associated with repeated inferior limit and requires no compactness, which makes it suitable critical cases. Then by abstract theorem, verify attractor estimate its attractive speed wave equation nonlocal damping, ant...

In this paper, we study the problem concerning stability and asymptotic behaviours of solutions for a degenerate Landau-Lifshitz equation in micromagnetics involving only the nonlocal magnetostatic energy. Due to the lack of derivative estimates, we do not have the compactness needed for strong convergence and the natural convergence is weak* convergence. By formulating the problem in a new fra...

We establish the existence of a nontrivial solution to systems of coupled Poisson equations with critical growth in unbounded domains. The proofs rely on a generalized linking theorem due to Krysewski and Szulkin [9], and on a concentration-compactness argument since the Palais-Smale condition fails at all critical levels. Mathematical Subject Classification. 35J50, 35J55

Existence of global weak solutions to a spatially inhomogeneous kinetic model for coalescing particles is proved, each particle being identified by its mass, momentum and position. The large time convergence to zero is also shown. The cornestone of our analysis is that, for any nonnegative and convex function, the associated Orlicz norm is a Liapunov functional. Existence and asymptotic behavio...

The existence and regularity of Young measure-valued solutions and weak solutions to non-Newtonian flows are considered. Galerkin approximation and an L2 compactness theorem are main ingredients for the proof of the existence of Young measurevalued solutions. Under a certain convexity condition for the energy, we prove that Young measure-valued solutions are weak solutions. Also, for the limite...

We are concerned with the compactness in Lloc of the semigroup (St)t≥0 of entropy weak solutions generated by hyperbolic conservation laws in one space dimension. This note provides a survey of recent results establishing upper and lower estimates for the Kolmogorov ε-entropy of the image through the mapping St of bounded sets in L1 ∩ L∞, both in the case of scalar and of systems of conservatio...