The Cauchy problem of coupled elliptic sine-Gordon equations with noise: analysis of a general kernel-based regularization and reliable tools of computing

DOI10.1016/j.camwa.2016.11.001zbMath1368.65217arXiv1508.05432OpenAlexW2567533734MaRDI QIDQ2013715

Nguyen Ho Minh Duy, Vo Anh Khoa, Nguyen Huy Tuan, Mai Thanh Nhat Truong

Publication date: 9 August 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.05432

zbMATH Keywords

stabilityconvergence rateill-posednessregularization methodshighly oscillatory integralselliptic sine-Gordon equations

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Second-order semilinear hyperbolic equations (35L71) Boundary value problems for second-order elliptic systems (35J57) Initial-boundary value problems for second-order hyperbolic systems (35L53) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

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Cites Work

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• A modified integral equation method of the nonlinear elliptic equation with globally and locally Lipschitz source
• Bound states of the elliptic sine-Gordon equation
• On an inverse boundary value problem of a nonlinear elliptic equation in three dimensions
• A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
• Numerical approximation of vector-valued highly oscillatory integrals
• A stability estimate for ill-posed elliptic Cauchy problems in a domain with corners
• A numerical solution of the coupled sine-Gordon equation using the modified decomposition method
• On quadrature methods for highly oscillatory integrals and their implementation
• About stability and regularization of ill-posed elliptic Cauchy problems: the case of Lipschitz domains
• IDENTIFICATION PROBLEMS OF DAMPED SINE-GORDON EQUATIONS WITH CONSTANT PARAMETERS
• Conditional Stability Estimates and Regularization with Applications to Cauchy Problems for the Helmholtz Equation
• Approximation of mild solutions of the linear and nonlinear elliptic equations
• A non-local boundary value problem method for the Cauchy problem for elliptic equations
• The stability for the Cauchy problem for elliptic equations
• The Cauchy problem for Laplace's equation via the conjugate gradient method
• Efficient quadrature of highly oscillatory integrals using derivatives
• Approximate solution of a Cauchy problem for the Helmholtz equation

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