{"id":289,"date":"2015-01-06T10:21:56","date_gmt":"2015-01-06T15:21:56","guid":{"rendered":"https:\/\/my.vanderbilt.edu\/pderesearch\/?page_id=289"},"modified":"2015-09-09T11:42:59","modified_gmt":"2015-09-09T16:42:59","slug":"pde-seminar-spring-15","status":"publish","type":"page","link":"https:\/\/my.vanderbilt.edu\/pderesearch\/pde-seminar-spring-15\/","title":{"rendered":"PDE Seminar Spring 2015"},"content":{"rendered":"<h3>Fridays, 4:10pm, Stevenson Center 1307<\/h3>\n<p>Date:\u00a0<strong>Friday, January 30, 2015<\/strong><\/p>\n<ul>\n<li>Speaker: \u00a0<strong>Jozsef Farkas, University of Stirling (UK)<\/strong><\/li>\n<li>Title:\u00a0<span style=\"font-size: 13px;line-height: 19px\">Steady state problems in structured population dynamics.<\/span><\/li>\n<\/ul>\n<ul>\n<li>Abstract:\u00a0<span style=\"font-size: 13px;line-height: 19px\">In this talk we will discuss the question of existence of non-trivial steady states of some partial differential equations, which are intended to model structured populations. We reformulate the steady state problem as an abstract eigenvalue problem coupled with a fixed-point problem. This approach allows us to formulate biologically relevant conditions for the existence of a positive steady state. We will discuss the steady state problem for models with monotone infinite dimensional nonlinearities, as well as for models with non-monotone finite dimensional nonlinearities.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-size: 13px\">Date: <\/span><strong>Friday, February 6, 2015<\/strong><\/p>\n<ul>\n<li>Speaker: \u00a0<strong>Der-Chen Chang,\u00a0Georgetown University, Washington DC <\/strong><\/li>\n<li>Title:\u00a0Analysis on Decoupled Domains in\u00a0<strong>C<\/strong><sup><strong>n<\/strong><\/sup><sup><strong> <\/strong><\/sup><\/li>\n<li>Abstract:\u00a0A domain \u03a9 in\u00a0<strong>C<\/strong><sup><strong>n<\/strong><\/sup> and its boundary \u2202\u03a9\u00a0are said to\u00a0be\u00a0<em>decoupled of finite type<\/em> if there exists\u00a0sub-harmonic, non-harmonic polynomials { P<sub>j<\/sub> }<sub>j=1,&#8230;,n<\/sub>, with P<sub>j<\/sub>(0) = 0, such that<br \/>\n\u03a9 = { (z<sub>1<\/sub>, &#8230;, z<sub>n<\/sub>, z<sub>n+1<\/sub>): Im(z<sub>n+1<\/sub>) &gt; P<sub>1<\/sub>(z<sub>1<\/sub>) + &#8230; + P<sub>n<\/sub>(z<sub>n<\/sub>) }.\u00a0 We call the integer m<sub>j<\/sub>=2+degree(\u00a0\u0394P<sub>j<\/sub>) the degree of P<sub>j<\/sub>. The &#8220;type&#8221; of \u03a9 is m=max{m<sub>1<\/sub>, &#8230;, m<sub>n<\/sub>}.<br \/>\nIn this talk, we use the method developed by Greiner-Stein and Chang-Nagel-Stein to construct the &#8220;fundamental solution&#8221; N for the \u2202 &#8211; bar Neumann problem on\u00a0\u03a9. Click <a href=\"http:\/\/www.math.vanderbilt.edu\/~disconmm\/PDE-Seminar\/Abstract_PDE_seminar_Feb_6_2015.pdf\">here<\/a> for a full abstract.<\/li>\n<\/ul>\n<p>Date:\u00a0<strong>Friday, February 20, 2015<\/strong><\/p>\n<ul>\n<li>Speaker: \u00a0<strong>Ugo Gianazza, University of Pavia (Italy)<\/strong><\/li>\n<li>Title: Boundary regularity for degenerate and singular parabolic equations<\/li>\n<li>Abstract:\u00a0I characterise regular boundary points of the parabolic p-Laplacian in terms of a family of barriers, both when p &gt; 2 and 1 &lt; p &lt; 2. By constructing suitable families of barriers, I give some simple geometric conditions that ensure the regularity of boundary points.<\/li>\n<\/ul>\n<p>Date:\u00a0<strong>Friday, March 13, 2015<\/strong><\/p>\n<ul>\n<li>Speaker: \u00a0<strong>Yuanzhen Shao, Vanderbilt University<\/strong><\/li>\n<li>Title:\u00a0Degenerate and singular elliptic operators on manifolds with singularites<\/li>\n<li>Abstract:\u00a0In this talk, we will establish the theory for a class of degenerate and singular elliptic operators on manifolds with singularities. Based on this theory, we investigate several linear and nonlinear parabolic equations arising from geometric analysis and degenerate boundary value problems. Emphasis will be given to geometric flows with &#8220;bad&#8221; initial metric.<\/li>\n<\/ul>\n<p><span style=\"font-size: 13px\">Date: <\/span><strong>Friday, March 20, 2015<\/strong><\/p>\n<ul>\n<li>Speaker: \u00a0<strong>Mathew Gluck, The University of Alabama in Huntsville<\/strong><\/li>\n<li>Title: Blow-up phenomena in elliptic and parabolic models<\/li>\n<li>Abstract: Click\u00a0<a href=\"http:\/\/www.math.vanderbilt.edu\/~disconmm\/PDE-Seminar\/Abstract_PDE_seminar_March_18_2015.pdf\">here<\/a> for an abstract.<\/li>\n<\/ul>\n<p>Date:\u00a0<strong>Thursday, April 23, <\/strong><strong>2015, <\/strong>SC 1432 at 1:10pm (notice the different day, time, and location).<\/p>\n<ul>\n<li>Speaker: \u00a0<strong>Mats Gyllenberg, University of Helsinki (Finland)<\/strong><\/li>\n<li>Title: When is a structured population model representable by a system of ordinary\u00a0differential equations?<\/li>\n<li>Abstract:\u00a0Models of physiologically structured populations are usually formulated in terms of PDEs with a nonlinear feedback through the environment, or as nonlinear Volterra integral equations. In both cases the resulting dynamical system is infinite-dimensional. Although basic questions like analysing steady states \u00a0and determining their local stability properties have been settled for the infinite dimensional dynamical system, many important questions remain. For instance, in what manner does the population state evolve with time and possibly reach a steady state? What is the structure of the omega-limit set? Because of the in finite dimensionality of the problem these questions are hard to answer in general. In contrast, there is a highly developed qualitative theory for systems of ordinary di erential equations, where such questions can be treated.\u00a0There are also highly efficient packages for solving systems of ODEs numerically, whereas corresponding methods for general structured population models are rare.Because of the arguments mentioned above, it is important to \u00a0find necessary and sufficient conditions for solutions of PDEs and\/or Volterra equations to be representable in terms of solutions of a system of ordinary di erential equations. This is the main purpose of my talk.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fridays, 4:10pm, Stevenson Center 1307 Date:\u00a0Friday, January 30, 2015 Speaker: \u00a0Jozsef Farkas, University of Stirling (UK) Title:\u00a0Steady state problems in structured population dynamics. Abstract:\u00a0In this talk we will discuss the question of existence of non-trivial steady states of some partial differential equations, which are intended to model structured populations. We reformulate the steady state problem&#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-289","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages\/289","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=289"}],"version-history":[{"count":21,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages\/289\/revisions"}],"predecessor-version":[{"id":338,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/pages\/289\/revisions\/338"}],"wp:attachment":[{"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/media?parent=289"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/pderesearch\/wp-json\/wp\/v2\/tags?post=289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}