{"id":3752,"date":"2014-12-01T17:57:59","date_gmt":"2014-12-01T13:57:59","guid":{"rendered":"http:\/\/www.imm.az\/exp\/?p=3752"},"modified":"2014-12-01T17:57:59","modified_gmt":"2014-12-01T13:57:59","slug":"announcement-5","status":"publish","type":"post","link":"https:\/\/www.imm.az\/exp\/2014\/12\/01\/announcement-5\/","title":{"rendered":"ANNOUNCEMENT"},"content":{"rendered":"<p style=\"text-align: justify;\">The weekly Wednesday seminar on 03 December 2014, 10.00 a.m., will feature Professor Varga Kalantarov (Department of Mathematics, Ko\u00e7 University, Turkey) who will talk about \u00abFinite-dimensional Asymptotic Behavior of Dynamical Systems Generated by Strongly Damped Nonlinear Wave Equations\u00bb.<\/p>\n<p style=\"text-align: justify;\">In this talk the problem of finite-dimensional asymptotic behavior (in time) of dynamical systems generated by initial boundary value problems for nonlinear strongly damped wave equation of the form<\/p>\n<p style=\"text-align: center;\"><em>u<sub>tt\u00a0<\/sub>+ f(u)u<em><sub>t\u00a0<\/sub>&#8211; b\u0394<em>u<em><sub>t<\/sub><\/em><\/em> &#8211;\u00a0<em><em>\u0394<em>u + g(u) = h, \u00a0 \u00a0 \u00a0<\/em><\/em><\/em><\/em>x\u00a0<\/em>\u2208\u03a9, \u00a0 \u00a0 <em>t &gt; 0<strong> \u00a0 <\/strong>(1)<\/em><\/p>\n<p style=\"text-align: justify;\">will be discussed. Here \u00a0 \u03a9 \u2282 R<sup>3<\/sup>\u00a0is a bounded domain with smooth boundary,\u00a0<em>b\u00a0<\/em>&gt; 0 is a given parameter, <em>h, f (\u2022), g\u00a0<em>(\u2022)\u00a0<\/em><\/em>are given functions.<\/p>\n<p style=\"text-align: justify;\">It will be show that under the standard smoothness and dissipativity restrictions on the nonlinear terms\u00a0<em>f(u)<\/em>\u00a0and\u00a0<em>g(u)\u00a0<\/em>the initial boundary value problem under the homogeneous Dirichlet boundary condition for the equation (1) is globally well-posed in the class of sufficiently regular solutions. We will show that the semigroup generated by the initial boundary value problem for the equation (1) has a global attractor in the corresponding phase space.<\/p>\n<p style=\"text-align: justify;\">In the case when\u00a0\u00a0<em>f(u)<\/em> = 0\u00a0we show that the asymptotic behavior (in time) of solutions of the initial boundary value problem for (1) is determined by finitely many Fourier modes.<\/p>\n<p style=\"text-align: justify;\">These results are obtained for the nonlinearities \u00a0<em>f(u)<\/em>\u00a0and\u00a0<em>g(u)\u00a0<\/em>of an arbitrary polynomial growth and without the assumption that the considered problem has a global Lyapunov function.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The weekly Wednesday seminar on 03 December 2014, 10.00 a.m., will feature Professor Varga Kalantarov (Department of Mathematics, Ko\u00e7 University, Turkey) who will talk about \u00abFinite-dimensional Asymptotic Behavior of Dynamical Systems Generated by Strongly Damped Nonlinear Wave Equations\u00bb. In this talk the problem of finite-dimensional asymptotic behavior (in time) of dynamical systems generated by initial [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[85,88],"tags":[],"_links":{"self":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts\/3752"}],"collection":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/comments?post=3752"}],"version-history":[{"count":1,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts\/3752\/revisions"}],"predecessor-version":[{"id":3753,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/posts\/3752\/revisions\/3753"}],"wp:attachment":[{"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/media?parent=3752"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/categories?post=3752"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.imm.az\/exp\/wp-json\/wp\/v2\/tags?post=3752"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}