ÿþ<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en"> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="GENERATOR" content="Mozilla/4.79 [en] (X11; U; SunOS 5.7 sun4u) [Netscape]"> <title>Xiao-Biao Lin's Web Page</title> </head> <body> <h1> Xiao-Biao Lin</h1> <h3> Professor</h3> <a href="http://www.math.ncsu.edu">Department of Mathematics</a>, <a href="http://www.ncsu.edu/">North Carolina State University</a>, <a href="http://www.newsobserver.com/">Raleigh, NC</a> 27695-8205<br> email: xblin@math.ncsu.edu,&nbsp;Telephone: 919 515 7440, Secretary: 919 515 2382, FAX: 919 515 3798&nbsp; <p></p> <hr><li><a href="http://www4.ncsu.edu/%7Exblin/photos/nintendo.jpg">Nintendo Headquarter, Redmond WA</a></li> <li><a href="http://www4.ncsu.edu/%7Exblin/photos/Lin,_XB.jpg">Old Photo</a></li> <li><a href="http://www4.ncsu.edu/%7Exblin/photos/playground.jpg">Young David before a soccer practice</a></li> <!--<li><a href="http://www4.ncsu.edu/%7Exblin/photos/soccermatch.jpg">challenge team, before a soccer match</a></li>--> <li><a href="http://www4.ncsu.edu/%7Exblin/photos/maui3.jpg">Maui Luau, Hawaii</a></li> <!--<li><a href="http://www4.ncsu.edu/%7Exblin/photos/trophy.jpg">Meet David Lin,</a></li>--> <!--<li><a href="http://www4.ncsu.edu/%7Exblin/photos/enloe1.jpg">Enloe High School Tennis Team,</a></li>--> <!--<li><a href="http://www4.ncsu.edu/%7Exblin/photos/pinehurst.jpg">Team Southern, Pinehurst NC,</a></li>--> <!--<li><a href="http://www4.ncsu.edu/%7Exblin/photos/double1.jpg">Double's Champion,</a></li>--> <li><a href="http://picasaweb.google.com/lh/photo/bDF_7eK0qrOKPC-VE-oXMg?feat=directlink">Lin and Robert O'Malley,</a></li> <li><a href="http://www4.ncsu.edu/%7Exblin/photos/linvangils.jpg">Lin and van Gils,</a></li> <li><a href="http://www4.ncsu.edu/%7Exblin/photos/bjornlinhale.jpg">Sandstede, Lin and Hale, 2008</a></li> <li><a href="http://www4.ncsu.edu/%7Exblin/hale80">Hale 80, Sao Carlos, 2008 </a></li> <li><a href="http://www4.ncsu.edu/%7Exblin/photos/zhang-zhi-feng.JPG">Zhang Zhifeng </a></li> <b><br> <!--<a href="http://www4.ncsu.edu/%7Exblin/scores.txt">Links</a></b> <p></p>--> <li><a href="http://www.ime.usp.br/~map/dhenry/">Dan Henry's Manuscripts</a></li> <b><br> <hr width="100%"> <h2>&nbsp;<a href="http://www4.ncsu.edu/%7Exblin/schedule2010s.pdf">Spring 2010 Schedule </a></h2> <li><a href="http://www4.ncsu.edu/%7Exblin/jordan.pdf">A geometric proof for the Jordan canonical form of a matrix </a></li> <li><a href="http://www4.ncsu.edu/%7Exblin/sturmliouville.pdf">STURM-LIOUVILLE THEORY, VARIATIONAL APPROACH </a></li> <li> <a href="http://www4.ncsu.edu/%7Exblin/ma444/Putnaminvit.doc">Invitation to Putnam Math Competition and MA444h </a></li> <li> <a href="http://www4.ncsu.edu/%7Exblin/ma591x/ma591x.html">MA591x Section 001 </a></li> <li> <a href="http://www4.ncsu.edu/%7Exblin/ma308/308.html">MA308 </a></li> <li> <a href="http://www4.ncsu.edu/%7Exblin/ma425">MA425 wrap dir </a></li> <li> <a href="http://www4.ncsu.edu/%7Exblin/ma532/532.html">MA532 Section 001</a></li> <li> <a href="http://www4.ncsu.edu/%7Exblin/ma732/732.html">MA732 Section 001</a></li> <li> <a href="http://www4.ncsu.edu/%7Exblin/MA493R.html">MA493R, Putnam Seminar</a></li> <hr width="100%"> <h2>&nbsp;<a href="http://maths.gzhu.edu.cn/conference091219/"> The Third International Conference on Recent Advances in Applied Dynamical Systems </a> &nbsp; Dec. 20-23, 2009, Guangzhou University, P.R. China </h2 <h2>&nbsp;<a href="http://math.scu.edu.cn/site2006/2009/english.html"> 2009 International Conference on Nonlinear and Stochastic Dynamics </a>&nbsp; June 1-5, 2009, Chengdu, P.R. China </h2> <hr width="100%"> <h2>&nbsp;<a href="http://www.fields.utoronto.ca/programs/scientific/08-09/dynsys/"> International Conference on Infinite Dimensional Dynamical Systems, Dedicated to Professor George Sell on the occasion of his 70th birthday </a>&nbsp; Sept 24-28, 2008, York University, Toronto, CA</h2> <hr width="100%"> <h2>&nbsp;<a href="http://www4.ncsu.edu/%7Exblin/preprint/jinhua08.pdf"> Workshop on Dynamical Systems and Nonlinear Waves,</a>&nbsp; May 29-June 5, 2008, Zhejiang Normal University, Jinhua, China. </h2> <hr width="100%"> <h2>&nbsp;<a href="http://www4.ncsu.edu/%7Exblin/preprint/shanghai.pdf"> Workshop on Bifurcation Methods of Limit Cycles and Related Studies, </a>&nbsp; May 20-29, 2008, Shanghai Normal University, Shanghai China. </h2> <hr width="100%"> <h2>&nbsp;<a href="http://www.icmc.usp.br/%7Esummer/summers/summer08/"> ICMC Summer Meeting on Differential Equations, 2008 Chapter. ,</a>&nbsp; January 28 to February 01, ICMC-USP, Sao Carlos SP, Brazil </h2> <hr width="100%"> <h2>&nbsp;<a href="http://www.math.wm.edu/~shij/conference/main.html"> The Second International Conference on Recent Advance in Applied Dynamical Systems. ,</a>&nbsp; June 4 -8, 2007, Zhejian Normal University, Jinhua, China </h2> <hr width="100%"> <h2>&nbsp;<a href="http://maths.gzhu.edu.cn/conference/">International Conference on Recent Developments in Differential Equations and Applications ,</a>&nbsp; July 17-21, 2006, Guangzhou University, China. </h2> <hr width="100%"> <h2>&nbsp;<a href="http://www.cirm.univ-mrs.fr/web.ang/liste_rencontre/Rencontres2005/Raugel05/adRaugel05.html">Systemes dynamiques en dimension infinie,</a>&nbsp; 4 au 8 juillet, 2005, Luminy, France</h2> <hr width="100%"> <h2>&nbsp;<a href="http://www.auburn.edu/%7Ewenxish/conference/">First International Conference on Recent Advances in Bifurcation Theory and Applications of Dynamical Systems,</a>&nbsp; June 8-12, 2005, JINHUA, CHINA</h2> <hr width="100%"> <h2>&nbsp;<a href="http://www.de2004.isikun.edu.tr">Workshop on Differential Equations and its Applications,</a>&nbsp; 15-17 September 2004, Istanbul Turkey</h2> <hr width="100%"> <h2><a href="http://intlpress.com/PDE/">Dynamics of Partial Differential Equations</a></h2> <hr width="100%"> <h2>&nbsp;<a href="http://www4.ncsu.edu/%7Exblin/wilmington.html">Traveling Waves and Shock Waves,</a>&nbsp; A special session in</h2> <h2> <a href="http://AIMsciences.org/Wilmington/Wilmington.htm">Fourth International Conference on Dynamical Systems and Differential Equations</a></h2> <hr width="100%"> <h2>Current Research Interests</h2> <ul> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/symbolicdynamics.pdf">Symbolic Dynamics and Nonlinear Semiflows </a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/delaydichotomy.pdf">Exponential dichotomies and homoclinic orbits in functional differential equations</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/delayheteroclinic.pdf">Heteroclinic orbits for reatrded functional differential equations</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/hale-lin-raugel.pdf">Upper Semicontinuity of Attractors for Approximations of Semigroups and Partial Differential Equations, By Jack K. Hale, Xiao-Biao Lin, and Geneviève Raugel</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/chowlinjohn.pdf">Transition layers for singularly perturbed delay differential equations with monotone nonlinearities </a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/NevesLin.pdf">A multiplicity theorem for hyperbolic systems</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/shadowsingper.pdf">Shadowing lemma and singularly perturbed boundary value problems</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/melnikovtosilnikov.pdf">Using Melnikov's method to solve Silnikov's problems</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/singular1990.pdf">Heteroclinic bifurcation and singularly perturbed boundary value problems</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/chowlulin.pdf">Smooth Invariant Folications in Infinite Dimensional Spaces</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/exponential-intermediate.pdf">Exponential Dichotomies in Intermediate Spaces with Applications to a Diffusively Perturbed Predator-Prey Model</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/twistedBifur.pdf">Twisted and nontwisted bifurcations induced by diffusion</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/groninge.pdf">Local and Global Existence of Multiple Waves Near Formal Approximations </a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/shadowmaterror.pdf">Shadowing matching errors for wave-front-like solutions, J. Differential Equations 129 (1996), 403-457. </a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/shock.pdf">Generalized Rankine-Hugoniot condition and shock solutions for quasilinear hyperbolic systems</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/multiple.pdf">Multiple Internal Layer Solutions Generated by Spatially Oscillatory Perturbations</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/formal.pdf">Construction and Asymptotic Stability of Structurally Stable Internal Layer Solutions</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/dynamo.pdf">Heteroclinic and periodic cycles in a perturbed convection model</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/stability.pdf">Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/minisurface.ps">Generalized Snell's law for weighted minimal surface in heterogeneous media</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/ejde.pdf">Multistage Evolutionary Model for Carcinogenesis Mutations</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/lai_li_lin.pdf">Fast solvers for 3D Poisson Equations Involving Interfaces in a Finite or Infinite Domain</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/sectorial.pdf">Analytic Semigroup Generated by the Linearization of a Riemann-Dafermos Solution</a></font></li> <li> <font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/sloweig.pdf">Slow Eigenvalues of Self-similar Solutions of the Dafermos Regularization of a System of Conservation Laws: an Analytic Approach</a></font></li> <li>&nbsp;<font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/hyperb.pdf">L2 Semigroup and Linear Stability for Riemann solutions of Hyperbolic Conservation Laws</a></font></li> <li>&nbsp;<font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/gearhart.pdf">Gearhart-Pruss theorem and linear stability for Riemann solutions of conservation laws </a></font></li> <li>&nbsp;<font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/algebra.pdf">Algebraic dichotomies and the stability of Riemann solutions of conservation laws </a></font></li> <li>&nbsp;<font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/ckdv.pdf">Travelling Wave Solutions for the Painleve-Integrable Coupled KdV Equations </a></font></li> <li>&nbsp;<font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/haitao510.pdf">Collapsing and explosion waves in phase transitions with metastability, existence, stability and related Riemann problems </a></font></li> <li> <font size="+1"> Xiao-Biao Lin (2008) <a href='http://www.scholarpedia.org/article/Lin%27s_method'>Lin's method</a>. <a href='http://www.scholarpedia.org'>Scholarpedia</a>, 3(9):6972 </font></li> <li>&nbsp;<font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/shooting.pdf">A Dynamical Systems Approach to Traveling wave solutions for liquid/vapor phase transition (2011)</a></font></li> <li>&nbsp;<font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/page1-lww.pdf">TravelingWave Solutions for a Predator Prey System With Sigmoidal Response Function, J. Dyn. Diff. Eqs., 23 (2011), 903-921.</a></font></li> <li>&nbsp;<font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/nozzle.pdf">Standing Waves for phase transitions in a spherically symmetric nozzle (2011)</a></font></li> <li>&nbsp;<font size="+1"><a href="http://www4.ncsu.edu/%7Exblin/preprint/wechselberger.pdf">TRANSONIC EVAPORATION WAVES IN A SPHERICALLY SYMMETRIC NOZZLE (2011)</a></font></li> </ul> <hr> <h2>Other Links</h2> <h2><a href="http://sites.google.com/site/shijiexiaoxue61">shijiexiaoxue-61-website</a></h2> <h2><a href="http://sites.google.com/a/sjxx61.info/sjxx61">www.sjxx61.info</a></h2> <h2><a href="http://www4.ncsu.edu/~xblin/music.html">Songs from the 1950s</a></h2> <table><tr><td><embed quality="high" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" width="301" height="280" src="http://res1.esnips.com/escentral/images/widgets/flash/white_player_list.swf" flashvars="autoPlay=no&amp;thePlayerURL=http://res1.esnips.com/escentral/images/widgets/flash/mp3WidgetPlayer.swf&amp;fileIds=904f0ffd-a1de-453f-beed-6a57b9a8621a;&amp;plURL=http://www.esnips.com//plxml/55442282-c9a8-4d1a-b01a-ab10ea62b5fd/?cachePL=true"></embed></td></tr><tr><td> Powered by <a target="_blank" style="color: #FF8000; font-weight:bold" href="http://www.esnips.com//adserver/?action=visit&cid=playlist_external"> eSnips.com </a></td></tr></table> <hr>Created:&nbsp; May 2001 <br> &nbsp; <br> &nbsp; <br> &nbsp; <!-- --><!-- --><!-- --> </ul> </body> </html>