- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 5 Issue: 4
- Note on abstract elliptic equations with nonlocal boundary in time condition
Note on abstract elliptic equations with nonlocal boundary in time condition
Authors : Kim Van HO THİ
Pages : 551-558
Doi:10.31197/atnaa.925768
View : 6 | Download : 1
Publication Date : 2021-12-30
Article Type : Research
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