Results 231 to 240 of about 19,509 (258)
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Geometric evolution equations in critical dimensions
Calculus of Variations and Partial Differential Equations, 2007There is a difference in the behaviours of two geometric evolution equations that otherwise show a lot of similarities: the harmonic map heat flow and the Yang-Mills heat flow. Equivariant solutions in the critical dimension can blow up for the former flow [\textit{K.-C. Chang, W.-Y. Ding} and \textit{R. Ye}, J.
Grotowski, J. F., Shatah, J.
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Symmetry and geometric evolution equations
Journal of Mathematical Sciences, 2006The author presents a purely analytical approach to geometric flows generated by some functions of principal curvatures. The approach is based on ideas and methods of the theory of nonlinear second order PDE.
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Numerical Approximation of Anisotropic Geometric Evolution Equations
2006We present a variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow, as well as related flows. The proposed scheme covers both the closed curve case, and the case of curves that are connected via triple junction points.
Barrett, John W. +2 more
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Numerical approximation of anisotropic geometric evolution equations in the plane
IMA Journal of Numerical Analysis, 2007We present a variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow, as well as related flows. The proposed scheme covers both the closed-curve case and the case of curves that are connected via triple junction points.
Barrett J. W., Garcke H., Nürnberg R.
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Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations
Journal of Physics A: Mathematical and General, 2003Summary: The known (2+1)-dimensional breaking soliton equation, the coupled KP equation with three potentials and a new (3+1)-dimensional nonlinear evolution equation are decomposed into systems of solvable ordinary differential equations with the help of the (1+1)-dimensional AKNS equations. The Abel-Jacobi coordinates are introduced to straighten out
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Integrable geometric evolution equations through a deformed Heisenberg spin equation
Journal of Geometry and PhysicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yoon, Dae Won +1 more
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Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019
Apart from three-dimensional continuum and discrete models, the evolution of surfaces is usually described by spatially two-dimensional partial differential equations (PDEs). These models are often derived from or at least motivated by small gradient approximations, but the studied surfaces do not fulfill this requirement in all cases.
C. Kabelitz, S. J. Linz
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Apart from three-dimensional continuum and discrete models, the evolution of surfaces is usually described by spatially two-dimensional partial differential equations (PDEs). These models are often derived from or at least motivated by small gradient approximations, but the studied surfaces do not fulfill this requirement in all cases.
C. Kabelitz, S. J. Linz
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Geometrical maps in the hydrodynamic/quantum description of the evolution equations
International Journal of Geometric Methods in Modern PhysicsIn this work, the topological and geometrical structure of the evolution equations of physical systems is treated and analyzed from the point of view of the set of solutions, in particular the singular ones. To this end, a generalization of the Wigner function is introduced for the case of multidimensional quadratic Hamiltonians of the type of our ...
Alexander I. Aptkarev +2 more
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