Exact solutions to a nonlinear partial differential equation: the Product-of-Curvatures Poisson \((u_{x x} u_{y y} = 1)\)

DOI10.1016/j.cam.2021.113866zbMath1505.35173OpenAlexW3206133640WikidataQ114201965 ScholiaQ114201965MaRDI QIDQ2074863

Yanyan Li

Publication date: 11 February 2022

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2021.113866

zbMATH Keywords

Dirichlet problemPCP equation

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Singular elliptic equations (35J75)

Cites Work

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• Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms
• Exact solutions of a nonlinear boundary value problem: The vortices of the two-dimensional sinh-Poisson equation
• The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
• A fast direct algorithm for the solution of the Laplace equation on regions with fractal boundaries
• New approximations to the principal real-valued branch of the Lambert \(W\)-function
• The Crane equation \(u u_{x x} = - 2\): the general explicit solution and a case study of Chebyshev polynomial series for functions with weak endpoint singularities
• On the Lambert \(w\) function
• Optimal truncations for multivariate Fourier and Chebyshev series: mysteries of the hyperbolic cross. I: bivariate case
• Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Equations II. Unbounded Domains
• Solving Transcendental Equations
• The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems
• Complex Singularities and the Lorenz Attractor
• Simple rotational flows
• The Blasius Function in the Complex Plane
• The Breakdown of Darboux's Principle and Natural Boundaries for a Function Periodised from a Ramanujan Fourier Transform Pair
• Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems
• Cubature, Approximation, and Isotropy in the Hypercube
• Sparse Spectral Approximations of High-Dimensional Problems Based on Hyperbolic Cross
• Numerical Methods for Special Functions
• Viscous and resistive eddies near a sharp corner