منابع مشابه
Blow-up of Solutions to the Generalized Inviscid Proudman-Johnson Equation
For arbitrary values of a parameter λ ∈ R, finite-time blowup of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of representation formulae for solutions to the problem. Mathematics Subject Classification (2010). 35B44, 35B10, 35B65, 35Q35.
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In this paper it is shown that the inviscid Burgers equation is nonlinearly self-adjoint. Then, from Ibragimov’s theorem on conservation laws, local conserved quantities are obtained. Mathematical subject classification: Primary: 76M60; Secondary: 58J70.
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For solutions of (inviscid, forceless, one dimensional) Burgers equation with random initial condition, it is heuristically shown that a stationary Feller-Markov property (with respect to the space variable) at some time is conserved at later times, and an evolution equation is derived for the infinitesimal generator. Previously known explicit solutions such as FrachebourgMartin’s (white noise ...
متن کاملThe Inviscid Limit of the Complex Ginzburg–Landau Equation
Naturally the question of inviscid limit arises. Does the solution u of the CGL equation (1.1) tend to (in an appropriate space norm) the solution v of the NLS equation (1.2) as the parameters a and b tend to 0? What is the convergence rate? The answers are not immediate especially when the initial data for these equations are not smooth. Because of its importance in both mathematical theory an...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 2009
ISSN: 0386-2194
DOI: 10.3792/pjaa.85.81