{"id":382,"date":"2016-06-12T18:34:33","date_gmt":"2016-06-12T23:34:33","guid":{"rendered":"https:\/\/my.vanderbilt.edu\/pderesearch\/?page_id=382"},"modified":"2016-11-03T08:04:34","modified_gmt":"2016-11-03T13:04:34","slug":"pde-seminar-fall-2016","status":"publish","type":"page","link":"https:\/\/my.vanderbilt.edu\/pderesearch\/pde-seminar-fall-2016\/","title":{"rendered":"PDE Seminar Fall 2016"},"content":{"rendered":"<h3>Fridays, 4:10pm, Stevenson Center 1307<\/h3>\n<p>Date:\u00a0<strong>Friday, August 26, 2016<\/strong><\/p>\n<ul>\n<li>Speaker: <strong>Chenyun Luo, Johns Hopkins University<\/strong><\/li>\n<li>Title:\u00a0On the motion of the free surface of a compressible liquid with vorticity.<\/li>\n<\/ul>\n<ul>\n<li>Abstract: I would like to go over some recent results on the compressible Euler equations with free boundary. We first provide a new apriori energy estimates which are uniform in the sound speed, which leads to the convergence to the solutions of the incompressible Euler equations.This is a joint work with Hans Lindblad. On the other hand, the energy estimates can be generalized to the compressible water wave problem, i.e., the domain that occupied by the fluid is assumed to be unbounded. Our method requires the detailed analysis of the geometry ofthe moving boundary<span style=\"font-size: 13px\">.<\/span><\/li>\n<\/ul>\n<p>Date:\u00a0<strong>Friday, September 9, 2016<\/strong><\/p>\n<ul>\n<li>Speaker:\u00a0<strong>Igor Kukavica, University of\u00a0Southern California<\/strong><\/li>\n<li>Title: On the existence and uniqueness of solutions to a fluid-structure system.<\/li>\n<\/ul>\n<ul>\n<li>Abstract: We address the system of partial differential equations\u00a0modeling motion of an elastic body inside an incompressible\u00a0fluid. The fluid is modeled by the incompressible\u00a0Navier-Stokes equations while the structure is represented\u00a0by the damped wave equation with interior damping. We will\u00a0review the local for large and global existence results for\u00a0small data. The global existence result is obtained for\u00a0small initial data in a suitable Sobolev space and is based\u00a0on an exponential decay of solutions. The results are joint\u00a0with M. Ignatova, I. Lasiecka, and A. Tuffaha.<\/li>\n<\/ul>\n<p>Date:\u00a0<strong>Friday, September 16, 2016<\/strong><\/p>\n<ul>\n<li>Speaker:\u00a0<strong>Yixiang Wu, Vanderbilt University<\/strong><\/li>\n<li>Title: Coexistence of competing species for intermediate dispersal rates in a reaction-di\ufb00usion chemostat model.<\/li>\n<\/ul>\n<ul>\n<li>Abstract: In this talk, we consider a di\ufb00usive chemostat model with two competing species. We \ufb01rst present various results on the single species model, and show that small diffusion rate is bene\ufb01cial to the species. We then prove the existence of stable steady states of the two species model within certain parameter ranges. We explore the dynamics of the model, including proving that there is no coexistence steady state when the di\ufb00usion rate is small. Our result demonstrates that coexistence is possible only for intermediate di\ufb00usion rates. This is joint work with Junping Shi from College of William and Mary and Xingfu Zou from University of Western Ontario.<\/li>\n<\/ul>\n<p>Date:\u00a0<strong>Friday, September 23, 2016<\/strong><\/p>\n<ul>\n<li>Speaker:\u00a0<strong>Abbas\u00a0Moameni,\u00a0Carleton University (Canada)<\/strong><\/li>\n<li>Title:New variational principles, convexity and supercritical\u00a0semi-linear Elliptic problems.<\/li>\n<\/ul>\n<ul>\n<li>Abstract:\u00a0The object of this talk is to present new variational\u00a0principles for certain differential equations.\u00a0These principles provide\u00a0new representations and formulations for the superposition of the gradient\u00a0of convex functions and symmetric operators.\u00a0They yield new variational resolutions for a large class of hamiltonian\u00a0partial differential equations with variety\u00a0of linear and nonlinear boundary conditions including many of the standard\u00a0ones. This approach seems to\u00a0offer several useful advantages: It associates to a boundary value problem\u00a0several potential functions which\u00a0can often be used with relative ease compared to other methods such as the\u00a0use of Euler-Lagrange functions.\u00a0These potential functions are quite flexible, and can be adapted to easily\u00a0deal with both nonlinear and\u00a0homogeneous boundary value problems. Additionally, in some cases, this\u00a0new method allows dealing with problems beyond the\u00a0usual locally compactness structure (problems with a supercritical Sobolev\u00a0nonlinearity).<\/li>\n<\/ul>\n<p><span style=\"font-size: 13px\">Date: <\/span><strong><span style=\"color: #3366ff\">Thursday,<\/span> October 6, 2016 (Notice the date: Colloquium on a PDE topic).<\/strong><\/p>\n<ul>\n<li>Speaker:\u00a0<strong>Lydia Bieri, University of Michigan<\/strong><\/li>\n<li>Title: The Einstein Equations and Gravitational Waves.<\/li>\n<\/ul>\n<ul>\n<li>Abstract:\u00a0In Mathematical General Relativity (GR) the Einstein equations describe the laws of the Universe. This system of hyperbolic nonlinear pde has served as a playground for all kinds of new problems and methods in pde analysis and geometry. A major goal in the study of these equations is to investigate the analytic properties and geometries of the solution spacetimes. In particular, fluctuations of the curvature of the spacetime, known as gravitational waves, have been a highly active research topic. Last year, gravitational waves were observed for the first time by LIGO. Understanding gravitational radiation is tightly interwoven with the study of the Cauchy problem in GR. I will talk about geometric-analytic results on gravitational radiation and the memory effect of gravitational waves. We will connect the mathematical findings to experiments. I will also address recent work with David Garfin- kle on gravitational radiation in asymptotically flat as well as cosmological spacetimes.<\/li>\n<\/ul>\n<p>Date:\u00a0<strong>Friday, October 7, 2016<\/strong><\/p>\n<ul>\n<li>Speaker: <strong>Giusy Mazzone,\u00a0Vanderbilt University<\/strong><\/li>\n<li>Title:Asymptotic Behavior of Rigid Bodies with a Liquid-Filled Gap.<\/li>\n<\/ul>\n<ul>\n<li>Abstract: Click <a href=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/1330\/2016\/06\/Giusy_Mazzone_abstract.pdf\">here<\/a>.<\/li>\n<\/ul>\n<p>Date:\u00a0<strong>Friday, October\u00a028, 2016<\/strong><\/p>\n<ul>\n<li>Speaker:\u00a0<strong>Georgi Kapitanov, University of Iowa<\/strong><\/li>\n<li>Title: Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model.<\/li>\n<\/ul>\n<ul>\n<li>Abstract: Post-traumatic osteoarthritis affects almost 20% of the adult US population. An injurious impact applies a significant amount of physical stress on articular cartilage and can initiate a cascade of biochemical reactions that can lead to the development of osteoarthritis. In our effort to understand the underlying biochemical mechanisms of this debilitating disease, we have constructed a multiscale mathematical model of the process with three components: cellular, chemical, and mechanical. The cellular component describes the different chondrocyte states according to the chemicals these cells release. The chemical component models the change in concentrations of those chemicals. The mechanical component contains a simulation of a blunt impact applied onto a cartilage explant and the resulting strains that initiate the biochemical processes. The scales are modeled through a system of partial-differential equations and solved numerically. The results of the model qualitatively capture the results of laboratory experiments of drop-tower impacts on cartilage explants. The model creates a framework for incorporating explicit mechanics, simulated by finite element analysis, into a theoretical biology framework. The effort is a step toward a complete virtual platform for modeling the development of post-traumatic osteoarthritis, which will be used to inform biomedical researchers on possible non-invasive strategies for mitigating the disease.<\/li>\n<\/ul>\n<p>Date:\u00a0<strong>Friday, November\u00a011, 2016<\/strong><\/p>\n<ul>\n<li>Speaker:\u00a0<strong>Elaine Cozzi, Oregon State University<\/strong><\/li>\n<li>Title: Incompressible Euler equations and the effect of changes at a distance.<\/li>\n<\/ul>\n<ul>\n<li>Abstract:\u00a0Because pressure is determined globally for the incompressible Euler equations, a localized change to the initial velocity will have an immediate effect throughout space. For solutions to be physically meaningful, one would expect such effects to decrease with distance from the localized change, giving the solutions a type of stability. One can easily show that this is the case for sufficiently smooth solutions having spatial decay. In this talk, we consider a broader class of weak solutions with vorticity lacking spatial decay, and we show that such stability still holds. This is based on joint work with James Kelliher.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fridays, 4:10pm, Stevenson Center 1307 Date:\u00a0Friday, August 26, 2016 Speaker: Chenyun Luo, Johns Hopkins University Title:\u00a0On the motion of the free surface of a compressible liquid with vorticity. Abstract: I would like to go over some recent results on the compressible Euler equations with free boundary. We first provide a new apriori energy estimates which&#8230;<\/p>\n","protected":false},"author":2740,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-382","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages\/382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/users\/2740"}],"replies":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/comments?post=382"}],"version-history":[{"count":23,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages\/382\/revisions"}],"predecessor-version":[{"id":417,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages\/382\/revisions\/417"}],"wp:attachment":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/media?parent=382"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/tags?post=382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}