一个扩散浅介质方程解的存在性
Existence of solutions to a diffusive shallow medium equation.
作者信息
Bögelein Verena, Dietrich Nicolas, Vestberg Matias
机构信息
Fachbereich Mathematik, Universität Salzburg, Hellbrunner Str. 34, 5020 Salzburg, Austria.
Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, 00076 Espoo, Finland.
出版信息
J Evol Equ. 2021;21(1):845-889. doi: 10.1007/s00028-020-00604-y. Epub 2020 Jul 25.
Abstract
In this article, we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First, we truncate the coefficients of the equation from above and below. Then, we prove convergence of the solutions of the truncated problem to a solution to the original equation.
摘要
在本文中，我们证明了浅介质方程弱解的存在性。我们通过逼近论证来进行。首先，我们从上下界截断方程的系数。然后，我们证明截断问题的解收敛到原方程的一个解。
相似文献
1
Existence of solutions to a diffusive shallow medium equation.一个扩散浅介质方程解的存在性
J Evol Equ. 2021;21(1):845-889. doi: 10.1007/s00028-020-00604-y. Epub 2020 Jul 25.
2
Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations.随机非线性输运方程的随机熵解
Entropy (Basel). 2018 May 23;20(6):395. doi: 10.3390/e20060395.
3
Existence and stability of the doubly nonlinear anisotropic parabolic equation.双重非线性各向异性抛物方程的存在性与稳定性
J Math Anal Appl. 2021 May 1;497(1):124850. doi: 10.1016/j.jmaa.2020.124850. Epub 2020 Dec 13.
4
A comparison principle for doubly nonlinear parabolic partial differential equations.双非线性抛物型偏微分方程的一个比较原理。
Ann Mat Pura Appl. 2024;203(2):779-804. doi: 10.1007/s10231-023-01381-4. Epub 2023 Sep 22.
5
A fixed-point approach for decaying solutions of difference equations.一种用于差分方程衰减解的不动点方法。
Philos Trans A Math Phys Eng Sci. 2021 Feb 22;379(2191):20190374. doi: 10.1098/rsta.2019.0374. Epub 2021 Jan 4.
6
Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations.退化抛物方程基于区域分解的时间积分器的收敛性分析
Numer Math (Heidelb). 2018;140(4):913-938. doi: 10.1007/s00211-018-0985-z. Epub 2018 Jul 7.
7
Higher integrability for doubly nonlinear parabolic systems.双重非线性抛物型系统的更高可积性。
SN Partial Differ Equ Appl. 2022;3(6):74. doi: 10.1007/s42985-022-00204-0. Epub 2022 Oct 18.
8
Acoustic shock wave propagation in a heterogeneous medium: a numerical simulation beyond the parabolic approximation.非均匀介质中声波冲击波的传播：超越抛物线近似的数值模拟。
J Acoust Soc Am. 2011 Jul;130(1):20-32. doi: 10.1121/1.3583549.
9
Weak and parabolic solutions of advection-diffusion equations with rough velocity field.具有粗糙速度场的对流扩散方程的弱解和抛物型解。
J Evol Equ. 2024;24(1):1. doi: 10.1007/s00028-023-00919-6. Epub 2023 Dec 16.
10
Analysis of Coupled Reaction-Diffusion Equations for RNA Interactions.RNA相互作用的耦合反应-扩散方程分析
J Math Anal Appl. 2015 May 1;425(1):212-233. doi: 10.1016/j.jmaa.2014.12.028.
Zotero 插件