infinite dimensional hamiltonian system

An infinite dimensional Hamiltonian system takes the form

(IHS)\\;\\;\\left\\{\\begin{array}[]{rll}\\partial_{t}u-\\Delta_{x}u&=H_{v}(t,x,u,v)&%\\\\-\\partial_{t}v-\\Delta_{x}v&=H_{u}(t,x,u,v)&\\forall(t,x)\\in\\mathbb{R}\\times%\\Omega\\end{array}\\right.

where $\\Omega\\subset{\\mathbb{R}}^{N}$ is a smoothly bounded domain, $H\\in\\mathcal{C}^{1}(\\mathbb{R}\\times\\overline{\\Omega}\\times\\mathbb{R}^{2},%\\mathbb{R})$ .

随便看

AppendixANotes
Appendix A Notes
ApplicationOfCauchyCriterionForConvergence
application of Cauchy criterion for convergence
ApplicationOfCauchySchwarzInequality
application of Cauchy–Schwarz inequality
ApplicationOfFundamentalTheoremOfIntegralCalculus
application of fundamental theorem of integral calculus
ApplicationOfLogarithmSeries
application of logarithm series
ApplicationOfSineIntegralAtInfinity
application of sine integral at infinity
ApplicationsOfSecondOrderRecurrenceRelationFormula
applications of second order recurrence relation formula
ApplicationsOfUrysohnsLemmaToLocallyCompactHausdorffSpaces
applications of Urysohn’s Lemma to locally compact Hausdorff spaces
ApplyingElementarySymmetricPolynomials
applying elementary symmetric polynomials
ApplyingGeneratingFunction
applying generating function
ApproximateIdentity
approximate identity
ApproximateNonlinearTransformationOfAffineCombination
approximate non-linear transformation of affine combination
ApproximatingAlgebraicNumbersWithLinearRecurrences

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。