Numerical Analysis of an Elliptic-Parabolic Partial Differential Equation [PDF]
, 1968 G. Fichera [1] and other authors have investigated partial differential equations of the form [Eq. 1.1] in which the matrix (aij(x)) is required to be semidefinite. Equations of this type occur in the theory of random processes.
Franklin, Joel N., Rodemich, Eugene R.
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Study of an elliptic partial differential equation modelling the Antarctic Circumpolar Current
Discrete and Continuous Dynamical Systems. Series A, 2019 We consider the ocean flow of the Antarctic Circumpolar Current. Using a recently-derived model for gyres in rotating spherical coordinates, and mapping the problem on the sphere onto the plane using the Mercator projection, we obtain a boundary-value ...
Susanna V. Haziot
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A partial differential equation for pseudocontact shift [PDF]
Physical Chemistry, Chemical Physics - PCCP, 2014 It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density.
Charnock, G.T.P., Kuprov, Ilya
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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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Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations
International Journal of Mathematics and Mathematical Sciences, 1989 The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic partial differential equations without use of linearizatlon techniques.
G. Adomian
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Differential-Difference Elliptic Equations with Nonlocal Potentials in Half-Spaces
Mathematics, 2023 We investigate the half-space Dirichlet problem with summable boundary-value functions for an elliptic equation with an arbitrary amount of potentials undergoing translations in arbitrary directions.
Andrey B. Muravnik
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The Extended Trial Equation Method for Some Time Fractional Differential Equations
Discrete Dynamics in Nature and Society, 2013 Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the ...
Yusuf Pandir +2 more
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Mathematics in Engineering, 2023 We discuss the design and implementation details of two conforming virtual element methods for the numerical approximation of two partial differential equations that emerge in phase-field modeling of fracture propagation in elastic material.
Yu Leng +6 more
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Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction [PDF]
, 2004 A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions.
Abraham +16 more
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