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26 papers · 1 filter
Numerical simulation of hydraulic fracturing: a hybrid FEM based algorithm
Michal Wrobel, Panos Papanastasiou, Daniel Peck
In this paper a problem of numerical simulation of hydraulic fractures is considered. An efficient algorithm of solution is proposed for the plain strain model of hydraulic fractur…
The Yang-Mills heat equation on three-manifolds with boundary
Nelia Charalambous
In this short note we provide an expository account of the work of Leonard Gross and the author on the Yang-Mills heat equation over smooth three-manifolds with boundary.
Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations
Olena Vaneeva, Vyacheslav Boyko, Alexander Zhalij +1
A class of the Newell-Whitehead-Segel equations (also known as generalized Fisher equations and Newell-Whitehead equations) is studied with Lie and "nonclassical" symmetry points o…
Poisson brackets after Jacobi and Plucker
Pantelis A. Damianou
We construct a symplectic realization and a bi-hamiltonian formulation of a 3-dimensional system whose solution are the Jacobi elliptic functions. We generalize this system and the…
Enhanced symmetry analysis of two-dimensional Burgers system
Stavros Kontogiorgis, Roman O. Popovych, Christodoulos Sophocleous
We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The complete point symmetry group of this system is found using an enhanced version of the algebraic me…
Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems
Pantelis A. Damianou, Charalampos A. Evripidou, Pavlos Kassotakis +1
Given a constant skew-symmetric matrix A, it is a difficult open problem whether the associated Lotka-Volterra system is integrable or not. We solve this problem in the special cas…