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具有加权吸收项的抛物型 - 拉普拉斯方程的完全淬灭现象

Complete quenching phenomenon for a parabolic -Laplacian equation with a weighted absorption.

作者信息

Zhu Liping

机构信息

College of Science, Xi'an University of Architecture & Technology, Xi'an, China.

出版信息

J Inequal Appl. 2018;2018(1):248. doi: 10.1186/s13660-018-1841-5. Epub 2018 Sep 20.

DOI:10.1186/s13660-018-1841-5
PMID:30839634
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC6154082/
Abstract

Throughout this paper, we mainly consider the parabolic -Laplacian equation with a weighted absorption in a bounded domain ( ) with Lipschitz continuous boundary subject to homogeneous Dirichlet boundary condition. Here and are parameters, and is a given constant. Under the assumptions , a.e. in Ω, we can establish conditions of local and global in time existence of nonnegative solutions, and show that every global solution completely quenches in finite time a.e. in Ω. Moreover, we give some numerical experiments to illustrate the theoretical results.

摘要

在本文中，我们主要考虑在有界区域(\Omega)（(\Omega\subset\mathbb{R}^n)，(n\geq1)）中具有加权吸收项的抛物 - 拉普拉斯方程，其边界为Lipschitz连续，且满足齐次狄利克雷边界条件。这里(\lambda)和(\mu)是参数，(f)是给定常数。在假设(\mu\geq0)，(f(x)\geq0)几乎处处在(\Omega)中的条件下，我们可以建立非负解的局部和全局时间存在性条件，并表明每个全局解在有限时间内几乎处处在(\Omega)中完全熄灭。此外，我们给出一些数值实验来说明理论结果。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/615a7240b67e/13660_2018_1841_Fig16_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/615a7240b67e/13660_2018_1841_Fig16_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/7d3eca7ad7b7/13660_2018_1841_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/bbf650e556f9/13660_2018_1841_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/e7b310bb5901/13660_2018_1841_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/de44e3dd6756/13660_2018_1841_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/3b361c34e18b/13660_2018_1841_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/a892c7dea8e2/13660_2018_1841_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/46167e2d604a/13660_2018_1841_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/ac885303002d/13660_2018_1841_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/ccf91c59929e/13660_2018_1841_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/b5abd17950c1/13660_2018_1841_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/f3a0ce013fc9/13660_2018_1841_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/5987c95c16d9/13660_2018_1841_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/c376b90d59c5/13660_2018_1841_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/096ecdb476ac/13660_2018_1841_Fig14_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/4f1573d0c2b4/13660_2018_1841_Fig15_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4884/6154082/615a7240b67e/13660_2018_1841_Fig16_HTML.jpg

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