Note on abstract elliptic equations with nonlocal boundary in time condition

Year 2021, Volume: 5 Issue: 4, 551 - 558, 30.12.2021

Kim Van Ho Thi

https://doi.org/10.31197/atnaa.925768

Abstract

Our main purpose of this paper is to study the linear elliptic equation with nonlocal in time condition. The problem is taken in abstract Hilbert space $H$. In concrete form, the elliptic equation has been extensively investigated in many practical areas, such as geophysics, plasma physics, bioelectric field problems. Under some assumptions of the input data, we obtain the well-posed result for the solution. In the first part, we study the regularity of the solution. In the second part, we investigate the asymptotic behaviour when some paramteres tend to zero.

Keywords

Cauchy problem, elliptic equations, well-posedness, regularity

Supporting Institution

Thu Dau Mot University

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