kaiyun開云官方網(wǎng)站學(xué)術(shù)講座

海 報(bào)

講座時(shí)間：03月26日（周三）,上午10: 30-11: 20

講座地點(diǎn)：X9301

主講人簡介：

  李新華，男，2020年于蘭州大學(xué)獲得博士學(xué)位，現(xiàn)為蘭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，主要從事無窮維動(dòng)力系統(tǒng)吸引子與慣性流形相關(guān)問題的研究。先后獲得國家自然科學(xué)基金青年基金，博士后面上基金，甘肅省青年基金的資助。曾獲甘肅省優(yōu)秀博士學(xué)位論文。在慣性流形、奇異耗散系統(tǒng)吸引子等相關(guān)研究中取得一些成果，部分成果已發(fā)表在SIAM J. Math.Anal.，J. Differential Equations, Proc.Amer. Math.Soc.等期刊。

講座內(nèi)容簡介：

報(bào)告題目：Finite-dimensional reduction and bi-Lipschitz embeddings of attractors for dissipative PDEs

摘要：The dynamics of a dissipative PDE can be reduced to a explicit system of ODEs by constructing inertial manifold. However, due to the required spectral gap condition, the known applications were mainly restricted to the PDEs defined on periodic domains with dimension two or three, and usually no longer valid for the space dimensions d≥4 or general bounded domains. In this talk, we introduce some theories of bi-Lipschitz Mane projections and provide a criterion which can realize the finite-dimensional reduction and deal with the case of multi-dimensional general bounded domains (aperiodic). As an example, we give the bi-Lipschitz Mane projections for a class of fractional Cahn-Hillard equations with Kirchhoff-type nonlinearity.

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