Events
Department of Mathematics and Statistics
Texas Tech University
We generalize Einstein’s probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected displacement per unit time with the velocity of the fluid, we derive an anisotropic diffusion equation in non-divergence form that contains a transport term. Under the Darcy law assumption, a corresponding nonlinear partial differential equations for the density function is obtained. The classical solutions of this equation are studied, and the maximum and strong maximum principles are established. We also obtain exponential decay estimates for the solutions for all time, and particularly, their exponential convergence as time tends to infinity. Our analysis uses some transformations of the Bernstein-Cole–Hopf type which are explicitly constructed even for very general equations of state. Moreover, the Lemma of Growth in time is proved and utilized in order to achieve the above decaying estimates.
This is joint work with Akif Ibragimov (Texas Tech University, and Oil and Gas Institute of the Russian Academy of Science).
In this talk, we explain the construction of models for twisted Spin(^c) bordism and its Anderson dual, in homotopy-theoretic, geometric, and differential settings. The talk is based on joint work with Yuanchu Li.In this talk, we discuss the almost complete intersection ring \(R\)
defined by \(n+1\) general quadrics in a polynomial ring in \(n\)
variables over a field \(\Bbbk\) and a corresponding linked Gorenstein
ring \(A\). Although these rings are not Koszul (except for some small
values of \(n\)), they have homological properties that extend those of
Koszul rings. This is joint work with Rachel Diethorn, Sema Gunturkun,
Pinar Mete, Liana Sega, Ola Sobieska, and Oana Veliche.
Join Zoom Meeting https://texastech.zoom.us/j/91729629174?pwd=TFJHbDk1ZS9KeTBRaldNL1hUbVNlQT09
Meeting ID: 937 0527 6265
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