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Explicit invariant solutions for invariant linear differential operators
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1984SynopsisLet F be a real analytic function on a real analytic manifold X. Let P be a linear differential operator on X such that , where Q is an ordinary differential operator with analytic coefficients whose singular points are all regular. For each (isolated) critical value z of F, we construct locally an F-invariant solution u of the equation Pu - v,
Szmydt, Zofia, Ziemian, Bogdan
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Group invariant solutions to a centro-affine invariant flow
Archiv der Mathematik, 2017The authors systematically study the group-invariant solutions of the centroaffine heat flow using Lie's theory of symmetry groups.
Weifeng Wo, Shuxin Yang, Xiaoliu Wang
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1986
When one is confronted with a complicated system of partial differential equations arising from some physically important problem, the discovery of any explicit solutions whatsoever is of great interest. Explicit solutions can be used as models for physical experiments, as benchmarks for testing numerical methods, etc., and often reflect the asymptotic
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When one is confronted with a complicated system of partial differential equations arising from some physically important problem, the discovery of any explicit solutions whatsoever is of great interest. Explicit solutions can be used as models for physical experiments, as benchmarks for testing numerical methods, etc., and often reflect the asymptotic
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Model of the Newtonian cosmology: Symmetries, invariant and partially invariant solutions
Communications in Nonlinear Science and Numerical Simulation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Klebanov, Igor, Startsun, O., Ivanov, S.
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Functionally invariant solutions to Maxwell’s system
Journal of Applied and Industrial Mathematics, 2017Summary: We consider the problem of the existence of functionally invariant solutions to Maxwell's system. The solutions found contain functional arbitrariness, which is used for determining the parameters of Maxwell's system (the dielectric and magnetic constants).
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Invariant Measures and Statistical Solutions
2016In this chapter we prove the existence of invariant measures associated with two-dimensional autonomous Navier–Stokes equations. Then we introduce the notion of a stationary statistical solution and prove that every invariant measure is also such a solution.
Grzegorz Łukaszewicz, Piotr Kalita
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Identifying invariant solutions with Nektar++
2022Several canonical flows are known to remain stable for arbitrary high values of the Reynolds numbers. In the case of those flows transition to turbulence is the result of the onset of equilibrium states, populating the phase space, rather than a cycle of bifurcations that takes the flow away from its laminar form.
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Making solution concepts invariant
1995Item does not contain ...
Vermeulen, A.J. +2 more
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Replication invariance of bargaining solutions
International Journal of Game Theory, 1986The author considers a bargaining problem, i.e. a problem of choosing a single output from the set S of possible outputs. An output is characterized by a sequence \(x_ 1,...,x_ n\) of utilities obtained by each of the n players. Without any loss of generality we can assume that a status quo point is \(x_ i=0\).
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