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Essential spectra of elliptic partial differential equations [PDF]
Bulletin of the American Mathematical Society, 1967 Let A be a closed, densely defined operator in a Banach space X. There are several definitions of the "essential" spectrum of A (cf. [ l ] , [2]). According to Wolf [3], [4] it is the complement in the complex plane of the $-set of A. The $-set $A of A is the set of points X for which (a) a(A — X), the dimension of the null space of A — X, is finite (b)
Martin Schechter
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On the Solutions of Quasi-Linear Elliptic Partial Differential Equations [PDF]
, 1938 The literature concerning these equations being very extensive, we shall not attempt to give a complete list of references. The starting point for many more modern researches has been the work of S.
Charles B. Morrey
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Journal of research of the National Bureau of Standards, 1980 In this report the combination of an iterative technique, the conjugate gradient algorithm, with a fast direct method, cyclic reduction, is used to solve the linear algebraic equations resulting from discretization of a nonseparable elliptic partial ...
John G. Lewis, R.G. Rehm
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Explicit and exact travelling wave solutions for Hirota equation and computerized mechanization. [PDF]
PLoS ONEBy using the power-exponential function method and the extended hyperbolic auxiliary equation method, we present the explicit solutions of the subsidiary elliptic-like equation.
Bacui Li, Fuzhang Wang, Sohail Nadeem
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An inverse problem for an elliptic partial differential equation
Journal of Mathematical Analysis and Applications, 1987 AbstractWe demonstrate uniqueness and local existence of the unknown coefficient a = a(x) in the elliptic equation Δu − a(x) u = 0 in the quarter plane x > 0, y > 0 which is subject to the boundary conditions u(0, y) = ƒ(y), ux(0, y) = g(y), and u(x, 0) = h(x).
John R. Cannon, William Rundell
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The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations
Abstract and Applied Analysis, 2014 Based on a nonlinear fractional complex transformation, the Jacobi elliptic equation method is extended to seek exact solutions for fractional partial differential equations in the sense of the modified Riemann-Liouville derivative.
Bin Zheng, Qinghua Feng
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Lectures on Elliptic Partial Differential Equations
, 2018 The volume develops several basic classical topics of the qualitative theory of elliptic partial differential equations and calculus of variations, including recent contributions to partial regularity for systems and the theory of viscosity solutions. The content is divided into the following five chapters: I.
Ambrosio, Luigi +2 more
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Learning Elliptic Partial Differential Equations with Randomized Linear Algebra [PDF]
Foundations of Computational Mathematics, 2021 Given input–output pairs of an elliptic partial differential equation (PDE) in three dimensions, we derive the first theoretically rigorous scheme for learning the associated Green’s function G .
N. Boull'e, Alex Townsend
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Study of an Elliptic Partial Differential Equation Modeling the Ocean Flow in Arctic Gyres
Journal of Mathematical Fluid Mechanics, 2021 We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential ...
Susanna V. Haziot
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A Solution Method for Differential Equations Based on Taylor PINN
IEEE Access, 2023 Based on deep neural network, elliptic partial differential equations in complex regions are solved. Accurate and effective strategies and numerical methods for elliptic partial differential equations are proposed by implementing deep feedforward ...
Yajuan Zhang +3 more
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