Asymptotic Analysis - Volume 127, issue 4

Authors: Dubois, François

Article Type: Research Article

Abstract: We propose a formal expansion of multiple relaxation times lattice Boltzmann schemes in terms of a single infinitesimal numerical variable. The result is a system of partial differential equations for the conserved moments of the lattice Boltzmann scheme. The expansion is presented in the nonlinear case up to fourth order accuracy. The asymptotic corrections of the nonconserved moments are developed in terms of equilibrium values and partial differentials of the conserved moments. Both expansions are coupled and conduct to explicit compact formulas. The new algebraic expressions are validated with previous results obtained with this framework. The example of isothermal D2Q9 …lattice Boltzmann scheme illustrates the theoretical framework. Show more

Keywords: Partial differential equations, asymptotic analysis

DOI: 10.3233/ASY-211692

Citation: Asymptotic Analysis, vol. 127, no. 4, pp. 297-337, 2022

Authors: Thanh Bui, Le Trong | Nguyen, Quoc-Hung

Article Type: Research Article

Abstract: In this paper, we give a short proof of the Lorentz estimates for gradients of very weak solutions to the linear parabolic equations with the Muckenhoupt class A q -weights u t − div ( A ( x , t ) ∇ u ) = div ( F ) , in a bounded domain Ω × ( 0 , T ) ⊂ R N + 1 , where A has a small mean oscillation, and Ω …is a Lipchistz domain with a small Lipschitz constant. Show more

Keywords: Quasilinear parabolic equations, maximal potential, Reifenberg flat domain

DOI: 10.3233/ASY-211693

Citation: Asymptotic Analysis, vol. 127, no. 4, pp. 339-353, 2022

Authors: Le, Hung

Article Type: Research Article

Abstract: In this paper, we consider a class of nonlocal equations where the convolution kernel is given by a Bessel potential symbol of order α for α > 1 . Based on the properties of the convolution operator, we apply a global bifurcation technique to show the existence of a highest, even, 2 π -periodic traveling-wave solution. The regularity of this wave is proved to be exactly Lipschitz.

Keywords: Whitham type, inhomogeneous, nonlocal, maximal height, water waves

DOI: 10.3233/ASY-211694

Citation: Asymptotic Analysis, vol. 127, no. 4, pp. 355-380, 2022

Authors: Zhang, Penghui | Yang, Lu

Article Type: Research Article

Abstract: In this paper, we study the long-time behavior of the following plate equation ε ( t ) u t t + g ( u t ) + Δ 2 u + λ u + f ( u ) = h , where the coefficient ε depends explicitly on time, the nonlinear damping and the nonlinearity both have critical growths.

Keywords: Plate equation, nonlinear damping, critical nonlinearity, time-dependent space

DOI: 10.3233/ASY-211698

Citation: Asymptotic Analysis, vol. 127, no. 4, pp. 381-397, 2022