Asymptotic Analysis - Volume 99, issue 3-4

Authors: Michalik, Sławomir | Podhajecka, Bożena

Article Type: Research Article

Abstract: We study the Stokes phenomenon for the solutions of the 1-dimensional complex heat equation and its generalizations with meromorphic initial data. We use the theory of Borel summability for the description of Stokes lines, anti-Stokes lines, jumps across Stokes lines, and a maximal family of the solutions.

Keywords: Stokes phenomenon, heat equation, Borel summability

DOI: 10.3233/ASY-161379

Citation: Asymptotic Analysis, vol. 99, no. 3-4, pp. 163-182, 2016

Authors: Colli, Pierluigi | Scarpa, Luca

Article Type: Research Article

Abstract: A rigorous proof is given for the convergence of the solutions of a viscous Cahn–Hilliard system to the solution of the regularized version of the forward-backward parabolic equation, as the coefficient of the diffusive term goes to 0. Non-homogenous Neumann boundary conditions are handled for the chemical potential and the subdifferential of a possible non-smooth double-well functional is considered in the equation. An error estimate for the difference of solutions is also proved in a suitable norm and with a specified rate of convergence.

Keywords: Cahn–Hilliard system, forward-backward parabolic equation, viscosity, initial-boundary value problem, asymptotic analysis, well-posedness

DOI: 10.3233/ASY-161380

Citation: Asymptotic Analysis, vol. 99, no. 3-4, pp. 183-205, 2016

Authors: Roamba, Brahima | de Dieu Zabsonré, Jean | Traoré, Sado

Article Type: Research Article

Abstract: This paper is devoted to the derivation and the study of a two-dimensional bilayer model. This model is obtained from the incompressible Navier–Stokes equations with suitable boundary conditions including friction and capillary effects as in the method used by [European J. Applied Mathematics 24 (6) (2013 ), 803–833] in the one dimensional case. We perform a multiscale analysis in space and time, as well as an asymptotic analysis to obtain a system coupling two different features: the Reynolds lubrication equations for the upper layer and the shallow water equation for the lower one. We finally prove the existence of …global weak solutions in time for model containing some additional terms. Show more

Keywords: bilayer models, Reynolds equation, shallow water equations, multiscale analysis, viscosity, friction, capillary effects

DOI: 10.3233/ASY-161381

Citation: Asymptotic Analysis, vol. 99, no. 3-4, pp. 207-239, 2016

Authors: Zhang, Fang-hong | Wang, Li-hong | Gao, Jin-ling

Article Type: Research Article

Abstract: In this paper, we investigate the long-time behavior of the solutions for the following nonclassical diffusion equations in locally uniform spaces u t − Δ u t − Δ u + f ( u ) = g ( x ) , x ∈ R N . First, we prove the well-posedness of solution for the nonclassical diffusion equations with critical nonlinearity in locally uniform spaces, and then the existence of ( H lu 1 ( R …N ) , H ρ 1 ( R N ) ) -global attractor is established. Finally, we obtain the asymptotic regularity of solutions which appears to be optimal and the existence of a bounded (in ( H lu 2 ( R N ) ) ) subset which attracts exponentially every initial H lu 1 ( R N ) -bounded set with respect to the H lu 1 ( R N ) -norm. Show more

Keywords: nonclassical diffusion equations, global attractor, asymptotic regularity, critical exponent, locally uniform spaces

DOI: 10.3233/ASY-161382

Citation: Asymptotic Analysis, vol. 99, no. 3-4, pp. 241-262, 2016

Article Type: Other

Citation: Asymptotic Analysis, vol. 99, no. 3-4, pp. 263-264, 2016