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 POROij PUST ꏊ PSVRRinzقVK~[eBORj u sG iEj u On type II blow-up mechanisms in the semilinear heat equation with critical Joseph-Lundgren exponent

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 XPPij PUST ꏊ PSVRRinzقVK~[eBORj u Professor Luca BonaventuraiPolitecnico di Milanoj u Semi-Lagrangian methods for diffusion problems uv| Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the semi-Lagrangian approach to diffusion and advection-diffusion problems have been proposed recently. These extensions are mostly based on probabilistic arguments and share the common feature of treating second-order operators in trace form, which makes them unsuitable for mass conservative models like the classical formulations of turbulent diffusion employed in computational fluid dynamics. I will present some joint work with R. Ferretti (University of Roma 3) in which we have proposed approaches treating second-order operators in divergence form. A general framework for constructing consistent schemes in one space dimension is presented, and specific cases of conservative and nonconservative discretization are discussed in detail and analyzed. Finally, an extension to (possibly nonlinear) problems in an arbitrary number of dimensions is proposed. Although the resulting discretization approach is only of first order in time, numerical results in a number of test cases highlight the advantages of these methods for applications to computational fluid dynamics and their superiority over to more standard low order time discretization approaches, for both the advection dominated and the stiff diffusion regimes.

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 WUi؁j PURO ꏊ PSVRRinzقVK~[eBORj u Professor Juhi Jang (University of Southern California, USA) u Dynamics of polytropic gaseous stars uv| I will discuss some mathematical problems arising from the dynamics of polytropic gaseous stars modeled by the Euler-Poisson system. Existence and stability theory of Lane-Emden equilibria will be presented.

 WRij PUST ꏊ PSVRRinzقVK~[eBORj u B Ǎs iEj u On Chorin's method for stationary solutions of the incompressible Navier-Stokes equation uv| To find a stationary solution of the incompressible Navier-Stokes equation, A. Chorin proposed an artificial compressible system which is obtained by adding the time derivative of the pressure $\epsilon \partial_t p$ to the continuity equation for the incompressible fluid, where $\epsilon>0$ is a small parameter. If the solution of the artificial compressible system converges to a stationary solution, then the stationary solution is also a stationary solution of the incompressible Navier-Stokes equation. By using this method, Chorin numerically obtained stationary cellular convection solutions of the Oberbeck-Boussinesq equation in a domain between two parallel plates. In this talk I will consider a mathematical justification of Chorin's method. It will be shown that if a stationary solution of the incompressible Navier-Stokes equation is asymptotically stable, then it is also asymptotically stable as a stationary solution of the artificial compressible system for sufficiently small $\epsilon$. Problem is formulated as a kind of singular perturbation problem. The point of the proof is to control the spectrum of the "compressbile part" of the linearized operator. This talk is based on a joint work with Takaaki Nishida (Kyoto university).

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 TPTij PUST ꏊ PSVRRinzقVK~[eBORj u 쎛 L iEhlhj u On a dynamical approach to an overdetermined problem in potential theory

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