Convergence of a Particle Method and Global Weak Solutions of a Family of Evolutionary PDEs

Autor:	Jian-Guo Liu, Terrance Pendleton, Alina Chertock
Rok vydání:	2012
Předmět:	Numerical Analysis Computational Mathematics Nonlinear system Applied Mathematics Weak solution Mathematical analysis Convergence (routing) Bounded variation Fluid dynamics Uniqueness Degasperis–Procesi equation Fluid transport Mathematics
Zdroj:	SIAM Journal on Numerical Analysis. 50:1-21
ISSN:	1095-7170 0036-1429
Popis:	The purpose of this paper is to provide global existence and uniqueness results for a family of fluid transport equations by establishing convergence results for the particle method applied to these equations. The considered family of PDEs is a collection of strongly nonlinear equations which yield traveling wave solutions and can be used to model a variety of flows in fluid dynamics. We apply a particle method to the studied evolutionary equations and provide a new self-contained method for proving its convergence. The latter is accomplished by using the concept of space-time bounded variation and the associated compactness properties. From this result, we prove the existence of a unique global weak solution in some special cases and obtain stronger regularity properties of the solution than previously established.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d9525e2d1324280143414f1343dad19a https://doi.org/10.1137/110831386 Zobrazit plný text záznamu