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On invariant solutions of the generalised boussinesq equation
International Journal of Engineering Science, 1988zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bhutani, O. P. +2 more
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Monotone Invariant Solutions to Differential Inclusions
Journal of the London Mathematical Society, 1977Abstract : Let a given set be endowed with a preference preordering, and consider the problem of finding a solution to a differential inclusion which remains in the given set and evolves monotonically with respect to the preordering. Sufficient conditions are given for the existence of such a trajectory, couched in terms of a notion of tangency ...
Clarke, Frank H., Aubin, J.-P.
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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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Maxwell's equations in Segal's model: Solutions and their invariance
Letters in Mathematical Physics, 1980We determine all smooth solutions of Maxwell's equation in Segal's universe; furthermore we show that the group of diffeomorphisms stabilizing the space of solutions of these equations is the conformal group of Segal's model.
Cahen, Michel, Gutt, Simone
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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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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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On the invariance of solutions of finite games
Mathematical Social Sciences, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vermeulen, A. J., Jansen, M. J. M.
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Maintaining Solution Invariants in the Numerical Solution of ODE
It is often desirable when numerically solving systems of ODEs to be able to conserve any invariance numerically, since the solution may be sensitive to small perturbations in these invariants. This paper considers a technique which can be used for nonlinear equality constraints which in effect turns the problem into a system of differential algebraic ...
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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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