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Asymptotic behavior of a sixth-order Cahn-Hilliard system

100%
EN
Our aim in this paper is to study the asymptotic behavior, in terms of finite-dimensional attractors, of a sixth-order Cahn-Hilliard system. This system is based on a modification of the Ginzburg-Landau free energy proposed in [Torabi S., Lowengrub J., Voigt A., Wise S., A new phase-field model for strongly anisotropic systems, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 2009, 465(2105), 1337–1359], assuming isotropy.
2
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The quasilinear parabolic kirchhoff equation

100%
EN
In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
EN
Large time behavior of the solution to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Furthermore, the rate of convergence is given. Initial-boundary value problem with mixed boundary conditions is considered.
4
76%
Open Mathematics
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2017
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tom 15
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nr 1
895-906
EN
The nonlinear diffusion equation of the ideal barotropic gas through a porous medium is considered. If the diffusion coefficient is degenerate on the boundary, then the solutions may be controlled by the initial value completely, the well-posedness of the solutions may be obtained without any boundary condition.
5
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Gradient estimates for inverse curvature flows in hyperbolic space

76%
EN
We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial hypersurface.
Open Mathematics
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2011
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tom 9
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nr 3
673-685
EN
In this paper the finite speed of propagation of solutions and the continuous dependence on the nonlinearity of a degenerate parabolic partial differential equation are discussed. Our objective is to derive an explicit expression for the speed of propagation and the large time behavior of the solution and to show that the solution continuously depends on the nonlinearity of the equation.
Open Mathematics
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2011
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tom 9
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nr 6
1435-1447
EN
This paper is mainly concerned with the blow-up and global existence profile for the Cauchy problem of a class of fully nonlinear degenerate parabolic equations with reaction sources.
8
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Integro-differential systems with variable exponents of nonlinearity

64%
EN
Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.
9
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Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

64%
Open Mathematics
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2010
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tom 8
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nr 3
548-568
EN
The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v 0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A 1, A 2,] with A 1 ≤ 0 ≤ A 2 so that the problem is of parabolic-hyperbolic type.
10
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Global φ-attractor for a modified 3D Bénard system on channel-like domains

52%
EN
In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.
Open Mathematics
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2012
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tom 10
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nr 6
1953-1968
EN
We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.
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