1D Impulsive Pseudoparabolic Equation with Convection and Absorption

IF 0.7 Q4 THERMODYNAMICS

Interfacial Phenomena and Heat Transfer Pub Date : 2023-01-01 DOI:10.1615/interfacphenomheattransfer.2023049787

Stanislav Antontsev, Ivan Kuznetsov, Sergey Sazhenkov

引用次数: 0

Abstract

We study the 1D initial-boundary value problem for the pseudoparabolic equation with a nonlinear convection term and a linear absorption term. The absorption term depends on a positive integer parameter $n$ and, as $n\to+\infty$, converges weakly$^\star$ to the expression incorporating the Dirac delta function, which models an instant absorption at the initial moment of time. We prove that the infinitesimal initial layer, associated with the Dirac delta function, is formed as $n\to+\infty$, and that the family of regular weak solutions of the original problem converges to the strong solution of a two-scale microscopic-macroscopic model. The main novelty of the article consists of taking into account of the effect of convection.

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具有对流和吸收的一维脉冲伪抛物方程

研究了具有非线性对流项和线性吸收项的伪抛物方程的一维初边值问题。吸收项取决于一个正整数参数$n$，并且，当$n\to+\infty$时，弱收敛于$^\star$包含狄拉克δ函数的表达式，该函数模拟了在初始时刻的瞬时吸收。证明了与狄拉克函数相关的无限小初始层形成为$n\to+\infty$，并证明了原问题的正则弱解族收敛于双尺度微观-宏观模型的强解。本文的主要新颖之处在于考虑了对流的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Interfacial Phenomena and Heat Transfer THERMODYNAMICS-

CiteScore

1.70

自引率

40.00%

发文量

期刊介绍： Interfacial Phenomena and Heat Transfer aims to serve as a forum to advance understanding of fundamental and applied areas on interfacial phenomena, fluid flow, and heat transfer through interdisciplinary research. The special feature of the Journal is to highlight multi-scale phenomena involved in physical and/or chemical behaviors in the context of both classical and new unsolved problems of thermal physics, fluid mechanics, and interfacial phenomena. This goal is fulfilled by publishing novel research on experimental, theoretical and computational methods, assigning priority to comprehensive works covering at least two of the above three approaches. The scope of the Journal covers interdisciplinary areas of physics of fluids, heat and mass transfer, physical chemistry and engineering in macro-, meso-, micro-, and nano-scale. As such review papers, full-length articles and short communications are sought on the following areas: intense heat and mass transfer systems; flows in channels and complex fluid systems; physics of contact line, wetting and thermocapillary flows; instabilities and flow patterns; two-phase systems behavior including films, drops, rivulets, spray, jets, and bubbles; phase change phenomena such as boiling, evaporation, condensation and solidification; multi-scaled textured, soft or heterogeneous surfaces; and gravity dependent phenomena, e.g. processes in micro- and hyper-gravity. The Journal may also consider significant contributions related to the development of innovative experimental techniques, and instrumentation demonstrating advancement of science in the focus areas of this journal.

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