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理學院迎百年校慶系列報告(二十六):Asymptotic behavior of the principal eigenvalue of a linear elliptic operator with small/large diffusion
[ 作者:理學院 來源:理學院 瀏覽:10 錄入時間:2020年08月11日 ]

 


報告時間:2020815日(周六)15:00 -- 16:00

報告地點:主樓203

報告題目:Asymptotic behavior of the principal eigenvalue of a linear elliptic operator with small/large diffusion

報告摘要: We shall report our recent progress on a principal eigenvalue problem of a linear second order elliptic operator with small/large diffusion. More specifically, we are concerned with the following eigenvalue problem: -D?φ -2α?m(x)?φ + V (x)φ = λφ in ?, complemented by a general boundary condition including Dirichlet boundary condition and Robin boundary condition: ?φ/?n + β(x)φ = 0 on ??, where β C(??) allows to be positive, sign-changing or negative, and n(x) is the unit exterior normal to ?? at x. The domain ?? R^N  is bounded and smooth, the constants D > 0 and α > 0 are, respectively, the diffusive and advection coefficients, and m C^2(?) , V C(?) are given functions. We aim to determine the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as the diffusive coefficient D → 0 or D → ∞. Our results, together with those by others where the Nuemann boundary case (i.e., β = 0 on ??) and Dirichlet boundary case were studied, reveal the important effect of advection and boundary conditions on the asymptotic behavior of the principal eigenvalue. The talk is based on a joint work with Guanghui Zhang and Maolin Zhou.

 

報告人簡介:彭銳,教授,博士生導師,江蘇省特聘教授,入選教育部新世紀優秀人才支持計劃, 獲得江蘇省杰出青年基金江蘇省數學成就獎,入選江蘇省“333人才工程中青年學科帶頭人。本科畢業于三峽大學,碩士畢業于東南大學,博士畢業于東南大學和澳大利亞新英格蘭大學,曾在加拿大紐芬蘭大學(AARMS資助)和美國明尼蘇達大學IMA(美國NSF資助)從事博士后工作德國洪堡學者獲得者。彭銳教授目前的主要研究興趣包括偏微分方程、動力系統理論以及在生物學、傳染病學和化學反應等領域的應用。已在Transactions of the American Mathematical Society、Journal of Functional Analysis、SIAM Journal on Mathematical Analysis、Indiana University Mathematics Journal、Journal of Nonlinear Science、Calculus of Variations and Partial Differential Equations、SIAM Journal on Applied Mathematics、Journal of Mathematical Biology、Physica D、Nonlinearity、European Journal of Applied Mathematics、Journal of Differential Equations等數學雜志發表學術論文多篇。

 


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