報(bào)告題目:Ground state for Schr?dinger-Poisson-Slater system with unbounded potential
報(bào)告人:王征平教授武漢理工大學(xué)
時(shí)間:9:00--9:40
Abstract
In this talk, we give some recent results on the existence of ground state for nonlinear Schr?dinger-Poisson-Slater equation with unbounded potential. By using Ekeland’s variational principle we prove that there exists a ground state with negative energy level. For the special case of Schr?dinger-Poisson-Slater equation with harmonic potential, we show that the ground state must be nonradial.
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報(bào)告二
報(bào)告題目:Existence and blow-up of ground state solutions for some Kirchhoff equations
報(bào)告人:張貽民教授武漢理工大學(xué)
時(shí)間:9:40--10:20
Abstract
For some Kirchhoff functionals, we search for its $L^2$-normalized critical points.Firstly, we give a complete classification with respect to the exponent $p$ for the existence of minimizers of these functionals, and show that the minimizer of these functionals, if exists, is unique up to translations. Secondly, we search for the mountain pass type critical point for these functionals on $L^2$ constraint manifold, and also prove that this type critical point is unique up to translations. Moreover, we get some blow up properties ground state solutions for this type Kirchhoff equations.
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報(bào)告三
報(bào)告題目:Ground states for some constraint variational problems
報(bào)告人:曾小雨副教授武漢理工大學(xué)
時(shí)間:10:20--11:00
Abstract
For some constraint variational problems, which arise in Bose-Einstein condensation and Bose star models, we study the existence and uniqueness of minimizers. Moreover, by employing some technical energy estimates, we investigate the limit behavior of minimizers as parameters go to the thresholds.
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報(bào)告四
報(bào)告題目:Convergence rate estimates for Alexandrov’s solution to the Monge-Ampere equation
報(bào)告人:黃耿耿副教授復(fù)旦大學(xué)
時(shí)間: 11:00--11:40
Abstract
In this talk, we talk about error estimates for solutions to the Dirichlet problem of the Monge-Ampere equation det D2u= inΩ, where f is a positive and continuous function andΩis a bounded convex domain in the Euclidean space Rn. We approximate the solution u by a sequence of convex polyhedra, which are generalised solutions to the Monge-Ampère equation in the sense of Aleksandrov, and the associated Monge- Ampère measures are supported on a properly chosen grid inΩ. We will derive error estimates for the cases when is smooth, H?lder continuous, and merely continuous. This is a joint work with Haodi Chen and Xu-Jia Wang.
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報(bào)告五
報(bào)告題目:ON THE VANISHING VISCOSITY LIMIT OF A CHEMOTAXIS MODEL
報(bào)告人:陳化教授武漢大學(xué)
時(shí)間:15:00--16:00
Abstract
A vanishing viscosity problem for the Patlak-Keller-Segel model is mentioned in this talk. This is a parabolic-parabolic system in a bounded domain, with a vanishing viscosity0. We show that if the initial value lies in W1,p with p> max {2; n}, then there exists a unique solution with its lifespan independent of. Furthermore, as converges to the solution of the limiting system in a suitable sense.
講座預(yù)告
2020年橢圓和拋物型偏微分方程進(jìn)展研討會(huì)
地 點(diǎn): 新波譜樓12樓1217報(bào)告廳
時(shí) 間: 2020年1月7日(周二)
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報(bào)告一
報(bào)告題目:Ground state for Schr?dinger-Poisson-Slater system with unbounded potential
報(bào) 告 人:王征平 教授 武漢理工大學(xué)
時(shí) 間: 9:00--9:40
Abstract
In this talk, we give some recent results on the existence of ground state for nonlinear Schr?dinger-Poisson-Slater equation with unbounded potential. By using Ekeland’s variational principle we prove that there exists a ground state with negative energy level. For the special case of Schr?dinger-Poisson-Slater equation with harmonic potential, we show that the ground state must be nonradial.
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報(bào)告二
報(bào)告題目:Existence and blow-up of ground state solutions for some Kirchhoff equations
報(bào) 告 人: 張貽民 教授 武漢理工大學(xué)
時(shí) 間: 9:40--10:20
Abstract
For some Kirchhoff functionals, we search for its $L^2$-normalized critical points.Firstly, we give a complete classification with respect to the exponent $p$ for the existence of minimizers of these functionals, and show that the minimizer of these functionals, if exists, is unique up to translations. Secondly, we search for the mountain pass type critical point for these functionals on $L^2$ constraint manifold, and also prove that this type critical point is unique up to translations. Moreover, we get some blow up properties ground state solutions for this type Kirchhoff equations.
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報(bào)告三
報(bào)告題目:Ground states for some constraint variational problems
報(bào) 告 人:曾小雨 副教授 武漢理工大學(xué)
時(shí) 間:10:20--11:00
Abstract
For some constraint variational problems, which arise in Bose-Einstein condensation and Bose star models, we study the existence and uniqueness of minimizers. Moreover, by employing some technical energy estimates, we investigate the limit behavior of minimizers as parameters go to the thresholds.
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報(bào)告四
報(bào)告題目:Convergence rate estimates for Alexandrov’s solution to the Monge-Ampere equation
報(bào) 告 人:黃耿耿 副教授 復(fù)旦大學(xué)
時(shí) 間: 11:00--11:40
Abstract
In this talk, we talk about error estimates for solutions to the Dirichlet problem of the Monge-Ampere equation det D2 u= in Ω, where f is a positive and continuous function and Ω is a bounded convex domain in the Euclidean space Rn. We approximate the solution u by a sequence of convex polyhedra , which are generalised solutions to the Monge-Ampère equation in the sense of Aleksandrov, and the associated Monge- Ampère measures are supported on a properly chosen grid in Ω. We will derive error estimates for the cases when is smooth, H?lder continuous, and merely continuous. This is a joint work with Haodi Chen and Xu-Jia Wang.
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報(bào)告五
報(bào)告題目:ON THE VANISHING VISCOSITY LIMIT OF A CHEMOTAXIS MODEL
報(bào) 告 人:陳化 教授 武漢大學(xué)
時(shí) 間: 15:00--16:00
Abstract
A vanishing viscosity problem for the Patlak-Keller-Segel model is mentioned in this talk. This is a parabolic-parabolic system in a bounded domain , with a vanishing viscosity 0. We show that if the initial value lies in W1,p with p> max {2; n}, then there exists a unique solution with its lifespan independent of . Furthermore, as converges to the solution of the limiting system in a suitable sense.
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報(bào)告六
報(bào)告題目::一類p-Laplace方程特征值問(wèn)題解的存在性與性態(tài)
報(bào) 告 人:周煥松 教授 武漢理工大學(xué)
時(shí) 間: 16:00--17:00
Abstract
本報(bào)告將主要介紹報(bào)告人及其合作者關(guān)于一類p-Laplace方程特征值問(wèn)題的相關(guān)研究結(jié)果。報(bào)告內(nèi)容主要包括應(yīng)用約束變分方法建立解的存在性以及利用能量估計(jì)的思想分析解的漸近行為。
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