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

Author

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  • Tuan, Nguyen Huy
  • Thang, Le Duc
  • Khoa, Vo Anh

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

Suggested Citation

  • Tuan, Nguyen Huy & Thang, Le Duc & Khoa, Vo Anh, 2015. "A modified integral equation method of the nonlinear elliptic equation with globally and locally Lipschitz source," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 245-265.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:245-265
    DOI: 10.1016/j.amc.2015.03.115
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    Cited by:

    1. Nguyen Anh Triet & Nguyen Duc Phuong & Van Thinh Nguyen & Can Nguyen-Huu, 2019. "Regularization and Error Estimate for the Poisson Equation with Discrete Data," Mathematics, MDPI, vol. 7(5), pages 1-20, May.
    2. Phuong, Nguyen Duc & Tuan, Nguyen Huy & Baleanu, Dumitru & Ngoc, Tran Bao, 2019. "On Cauchy problem for nonlinear fractional differential equation with random discrete data," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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