Existence of Solutions to the Poisson--Nernst--Planck System with Singular Permanent Charges in $\mathbb{R}^2$

Autor:	Chia-Yu Hsieh, Yong Yu
Rok vydání:	2022
Předmět:	Computational Mathematics Mathematics - Analysis of PDEs Applied Mathematics FOS: Mathematics Analysis Analysis of PDEs (math.AP)
Zdroj:	SIAM Journal on Mathematical Analysis. 54:1223-1240
ISSN:	1095-7154 0036-1410
DOI:	10.1137/21m1399841
Popis:	In this paper, we study the well-posedness of Poisson-Nernst-Planck system with no-flux boundary condition and singular permanent charges in two dimension. The main difficulty comes from the lack of integrability of singular permanent charges. In order to overcome the difficulty, the main idea is to transform the system into another weighted parabolic system. By choosing suitable weighted spaces, local existence of solutions can be obtained based on a fixed-point argument. Moreover, we also proved global existence by energy estimates under the smallness assumption on initial data. Comment: To appear in SIAM J. Math. Anal
Databáze:	OpenAIRE
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