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Group analysis of differential equations
Willard Miller,L. V. Ovsiannikov +1 more
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The article was published on 1982-01-01 and is currently open access. It has received 2925 citations till now. The article focuses on the topics: Stochastic partial differential equation & Numerical partial differential equations.read more
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The Porous Medium Equation: Mathematical Theory
TL;DR: The Porous Medium Equation (PME) as discussed by the authors is one of the classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood.
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New similarity reductions of the Boussinesq equation
TL;DR: In this paper, some new similarity reductions of the Boussinesq equation, which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering, are presented.
MonographDOI
The Porous Medium Equation
TL;DR: In this article, the authors introduced the notion of L1-limit solutions for the Dirichlet problem with nonhomogeneous data g 6 = 0 and showed that the L1 norm is a well-defined element of the L∞(Ω) space.
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Moving Coframes: II. Regularization and Theoretical Foundations
Mark E. Fels,Peter J. Olver +1 more
TL;DR: In this article, the authors provide a rigorous theoretical justification of Cartan's method of moving frames for arbitrary finite-dimensional Lie group actions on manifolds, which is of both theoretical and practical use.
Book
Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics
TL;DR: In this paper, a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium.