Asymptotic Analysis - Volume 127, issue 3

Authors: del Teso, Félix | Endal, Jørgen | Lewicka, Marta

Article Type: Research Article

Abstract: We propose two asymptotic expansions of two interrelated integral-type averages, in the context of the fractional ∞ -Laplacian Δ ∞ s for s ∈ ( 1 2 , 1 ) . This operator has been introduced and first studied in (Comm. Pure Appl. Math. 65 (2012) 337–380). Our expansions are parametrised by the radius of the removed singularity ε , and allow for the identification of Δ ∞ s ϕ ( x ) as the ε 2 …s -order coefficient of the deviation of the ε -average from the value ϕ ( x ) , in the limit ε → 0 + . The averages are well posed for functions ϕ that are only Borel regular and bounded. Show more

Keywords: Mean value formulas, nonlocal gradient dependent operators, fractional infinity Laplacian

DOI: 10.3233/ASY-211686

Citation: Asymptotic Analysis, vol. 127, no. 3, pp. 201-216, 2022

Authors: Jorge Silva, Marcio A. | Pinheiro, Sandro B.

Article Type: Research Article

Abstract: We address a Timoshenko system with memory in the history context and thermoelasticity of type III for heat conduction. Our main goal is to prove its uniform (exponential) stability by illustrating carefully the sensitivity of the heat and history couplings on the Timoshenko system. This investigation contrasts previous insights on the subject and promotes a new perspective with respect to the stability of the thermo-viscoelastic problem carried out, by combining the whole strength of history and thermal effects.

Keywords: Timoshenko system, exponential stability, history, type III thermoelasticity

DOI: 10.3233/ASY-211688

Citation: Asymptotic Analysis, vol. 127, no. 3, pp. 217-248, 2022

Authors: Muñoz Rivera, Jaime | Poblete, Verónica | Vera, Octavio

Article Type: Research Article

Abstract: We consider an Klein–Gordon relativistic equation with a boundary dissipation of fractional derivative type. We study of stability of the system using semigroups theory and classical theorems over asymptotic behavior.

Keywords: Semigroup theory, Klein–Gordon equation, polynomial stability

DOI: 10.3233/ASY-211689

Citation: Asymptotic Analysis, vol. 127, no. 3, pp. 249-273, 2022

Authors: De la cruz, Richard | Juajibioy, Juan

Article Type: Research Article

Abstract: In this paper, we propose a time-dependent viscous system and by using the vanishing viscosity method we show the existence of solutions for the Riemann problem to a particular 2 × 2 system of conservation laws with linear damping.

Keywords: Nonstrictly hyperbolic system, linear damping, Riemann problem, time-dependent viscous system, delta shock wave solution

DOI: 10.3233/ASY-211690

Citation: Asymptotic Analysis, vol. 127, no. 3, pp. 275-296, 2022