Two regularized solutions of an ill-posed problem for the elliptic equation with inhomogeneous source | Zendy

Nguyen Huy Tuan | Zendy; Binh Tran | Zendy

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Two regularized solutions of an ill-posed problem for the elliptic equation with inhomogeneous source

Author(s) -

Nguyen Huy Tuan,

Binh Tran

Publication year - 2014

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1410091t

Subject(s) - mathematics , a priori and a posteriori , well posed problem , cauchy problem , convergence (economics) , cauchy distribution , initial value problem , elliptic curve , mathematical analysis , philosophy , epistemology , economics , economic growth

In this paper, we address a Cauchy problem for elliptic equations with inhomoge- neous source data. The problem is shown to be ill-posed as the solution exhibits an unstable dependence on the given data functions. Here, we shall deal with this problem by using two di erent regularized methods. Moreover, convergence estimates are established under some priori assumptions on the exact solution. Some numerical examples are given to illuminate the e ect of our methods. Keywords and phrases: Cauchy problem; Ill-posed problem; Convergence estimates. Mathematics subject Classification 2000: 35K05, 35K99, 47J06, 47H10

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