<div dir="ltr"><div class="gmail_default" style="font-size:12.8000001907349px"><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><font size="4">The Department of Mathematics</font></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><font size="4">School of Science and Engineering</font></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><font size="4"> </font></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><font size="4">invites you to the PhD Thesis Defense of </font></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><font size="4"><br></font></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><b><font size="4">Mr. Mark Anthony C. Tolentino</font></b></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large"><br></span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large"><b>Title</b>:<b> </b>On the Lifespan of Solutions to Nonlinear Cauchy Problems with Small Analytic Data</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large"><br></span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Date:  August 22, 2015, Saturday</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Time:  10:00 am </span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Venue:  SEC-A303</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large"><br></span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Adviser:  Emmanuel A. Cabral, Ph.D.</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large"><br></span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Panelists:</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Flordeliza F. Francisco, Ph.D. (AdMU)</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Jose Ernie C. Lope, Ph.D. (UP-Diliman)</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Job A. Nable, Ph.D. (AdMU)</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Adrian Roy L. Valdez, Ph.D. (UP-Diliman)</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large"><br></span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">Abstract</span></div><div class="gmail_default" style="font-family:georgia,serif;font-size:12.8px;text-align:center"><span style="font-size:large">The paper studies the lifespan of solutions to Cauchy problems involving nonlinear analytic partial differential equations with small analytic data.  It is proved that the lifespan of the solution becomes longer as the initial data become smaller.  The dependence of the lifespan on the smallness of the data can be sharply described by a particular property of the equation.</span></div><div style="font-family:georgia,serif"><font size="4"><br></font></div></div></div>