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Solving the Biharmonic Equation as Coupled Finite Difference Equations
SIAM Journal on Numerical Analysis, 1971A technique is proposed for solving the finite difference biharmonic equation as a coupled pair of harmonic difference equations. Essentially, the method is a general block SOR method with convergence rate $O(h^{{1 / 2}} )$ on a square, where h is mesh size.
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Germain and Her Biharmonic Equation
2020What prompted Sophie Germain to enter the prize competition to derive a theory for vibrating surfaces? Did she see the contest as a source of mathematical knowledge and sought to advance her own intellectual development?
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TH-collocation for the biharmonic equation
Advances in Engineering Software, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Díaz, Martín, Herrera, Ismael
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Null Boundary Controllability for Biharmonic Heat Equation
Journal of Dynamical and Control SystemszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oner, Isil, Ismailov, Mansur I.
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On transformations of the biharmonic equation
Mathematika, 1985Consider a point transformation of the biharmonic equation \[ (\partial^ 2/\partial x^ 2+\partial^ 2/\partial y^ 2)^ 2\chi (x,y)=0, \] namely a coordinate transformation \(\xi =\xi (x,y)\), \(\eta =\eta (x,y)\), together with a change of dependent variable given by \(\chi (x,y)=F(\xi,\eta) \phi (\xi,\eta),\) for some multiplier F(\(\xi\),\(\eta)\).
Bluman, George W., Gregory, R. Douglas
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Biharmonic equations with asymptotically linear nonlinearities
Acta Mathematica Scientia, 2007Abstract This article considers the equation Δ2u = f(x,u) with boundary conditions either u|∂Ω= ∂ u ∂ n | ∂ Ω = 0 or u|∂Ω= Δu|∂Ω=0, where f(x,t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in RN, N >4.
Yue Liu, Zhengping Wang
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An Indirect Boundary Integral Equation Method for the Biharmonic Equation
SIAM Journal on Numerical Analysis, 1994An indirect boundary integral equation method for solving the Dirichlet problem for the biharmonic equation is proposed. For the numerical solution, a discrete Galerkin method is used and a complete numerical analysis in a suitable Sobolev space is given.
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Boundary Elements and the Biharmonic Equation
1992Possibly the most exciting development in applied numerical methods over the last fifteen years has been the popularization of “boundary element” methods. This modern engineering analysis technique has evolved from the much older mathematical subjects of integral equations, Green’s’ functions, and potential theory.
Charles V. Camp, G. Steven Gipson
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p‐Biharmonic Equation Involving Choquard Nonlinearity
Mathematical Methods in the Applied SciencesABSTRACT In this article, we study the ‐biharmonic equation involving Choqurd type nonlinearity with sign‐changing weight functions in a bounded domain with Dirichlet boundary condition. Using the Nehari manifold and fibering map analysis, we show the multiplicity results in subcritical case and existence results in critical case ...
Anu Rani, Sarika Goyal
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