The numerical solution of elliptic and parabolic partial differential equations with boundary singularities [PDF]
, 1976 A general numerical method is described for the solution of linear elliptic and parabolic partial differential equations in the presence of boundary singularities.
Furzeland, RM, Crank, J
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The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system)
Boundary Value Problems, 2020 In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain the shape of the new kind of the non-star ...
Bingyu Kou, Tianqing An, Zeyan Wang
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Weyl groups and elliptic solutions of the WDVV equations [PDF]
, 2010 A functional ansatz is developed which gives certain elliptic solutions of the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations. This ansatz is based on the elliptic trilogarithm function introduced by Beilinson and Levin. For this to be a solution
Ian A. B. Strachan, Strachan, I.A.B.
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(Revised) The numerical solution of elliptic and parabolic partial differential equations with boundary singularities [PDF]
, 1977 A general numerical method is described for the solution of linear elliptic and parabolic partial differential equations in the presence of boundary singularities.
Furzeland, RM, Crank, J
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Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients [PDF]
, 2013 This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and
Mikhailov, SE +2 more
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Distributed Control of Systems Governed by a General Class of Quasilinear Elliptic Equations
Journal of Differential Equations, 1993 Let \(\Omega\) be a bounded open subset of \(\mathbb{R}^ N\) with Lipschitz continuous boundary; let \(a: \Omega\times \mathbb{R}^ N\to \mathbb{R}^ N\), \(a_ 0: \Omega\times\mathbb{R}\to \mathbb{R}\) be two Carathéodory functions, \(C^ 1\) in the second variable, such that \[ \sum_{i,j=1}^ N \partial_{N+i} a_ j (.,\eta) \xi_ i\xi_ j\geq \Lambda_ 1(k+| \
Casas, E., Fernandez, L.A.
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Analysis of two-operator boundary-domain integral equations for variable-coefficient mixed BVP [PDF]
, 2011 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 Steklov Mathematical Institute RAS.Applying the two-operator approach, the mixed (Dirichlet–Neumann) boundary value ...
Mikhailov, SE, Ayele, TG
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Multivalued solutions of multidimensional linear equations of heat conduction and rivertons
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2021 Background. The article considers the problem of calculating multivalued solutions of multidimensional linear parabolic equations. Solutions for this type of equations of heat conductivity in dimension d > 2 were not previously known and represent an ...
V.M. Zhuravlev, V.M. Morozov
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Alexandria Engineering Journal, 2020 In this work, a cubic B-spline method based on finite difference and meshless approaches for solving 2D generalized telegraph equations in irregular single and multi-connected domains is presented.
Sergiy Reutskiy +3 more
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New elliptic system and global solutions for the constraints equations in General relativity [PDF]
Communications in Mathematical Physics, 1971 By a new choice of the arbitrarily given quantities on an initial 3-manifold we reduce the system of constraints, in General Relativity, to an elliptic system of four equations, the coefficients of which have a simple geometric interpretation on the 3-manifold. The system seems well suited for a global study and some results are given in this direction.
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