A modified integral equation method of the nonlinear elliptic equation with globally and locally Lipschitz source

Nguyen Huy Tuan, Le Duc Thang and Vo Anh Khoa

Applied Mathematics and Computation, 2015, vol. 265, issue C, 245-265

Abstract: The paper is devoted to investigating a Cauchy problem for nonlinear elliptic PDEs in the abstract Hilbert space. The problem is hardly solved by computation since it is severely ill-posed in the sense of Hadamard. We shall use a modified integral equation method to regularize the nonlinear problem with globally and locally Lipschitz source terms. Convergence estimates are established under priori assumptions on exact solution. A numerical test is provided to illustrate that the proposed method is feasible and effective. These results extend some earlier works on a Cauchy problem for elliptic equations

Keywords: Cauchy problem; Nonlinear elliptic equation; Ill-posed problem; Error estimates (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:245-265

DOI: 10.1016/j.amc.2015.03.115

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