<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN">
<html><body style='font-family: Verdana,Geneva,sans-serif'>
<p> </p>
<p>-------- Mensaje original --------</p>
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr><th align="right" valign="baseline" nowrap="nowrap">Asunto:</th>
<td>Coloquio del Departamento de Matemática -- jueves 25/8, 11:00 hs, Aula 5 -- Julio Rossi (UBA)</td>
</tr>
<tr><th align="right" valign="baseline" nowrap="nowrap">Fecha:</th>
<td>2016-08-19 12:45</td>
</tr>
<tr><th align="right" valign="baseline" nowrap="nowrap">Remitente:</th>
<td>Coloquio del Departamento de Matemática <coloquiodm@mate.unlp.edu.ar></td>
</tr>
<tr><th align="right" valign="baseline" nowrap="nowrap">Destinatario:</th>
<td>grad@mate.unlp.edu.ar, "docentes@mate.unlp.edu.ar" <docentes@mate.unlp.edu.ar>, "secre2@fisica.unlp.edu.ar" <secre2@fisica.unlp.edu.ar>, Alumnos <alumnosm@gmail.com>, info@exactas.unlp.edu.ar</td>
</tr>
</tbody>
</table>
<p> </p>
<!-- html ignored --><!-- head ignored --><!-- meta ignored -->
<div dir="ltr">
<div style="font-size: 12.8px;"><span style="font-size: small;">Hola a todos,</span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;"><br /></span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;">el próximo jueves 25 de agosto continuaremos con las reuniones </span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;">periódicas <span>del</span> <span>Coloquio</span> <span>del</span> Departamento de Matemática.</span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;">En esta ocasión, la charla estará a cargo de</span></div>
<a href="http://mate.dm.uba.ar/~jrossi/">Julio Rossi</a><span style="font-size: 12.8px;"> (UBA)</span>
<div style="font-size: 12.8px;"> </div>
<div style="font-size: 12.8px;">
<div class="gmail_extra">
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;">La información completa es la siguiente:</span></span></div>
<div><span style="font-size: 12.8px; background-color: rgba;"><br /></span>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;"><strong>Día:</strong> jueves 25 de agosto</span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;"><strong>Hora:</strong> 11:00 hs </span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;"><strong>Aula:</strong> Aula 5, <span>Departamento</span> de Matemática.</span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;"><br /></span></span></div>
<div><span style="font-size: 12.8px;"><span style="background-color: rgba;"><strong>Expositor: </strong>Julio Rossi (UBA)</span></span></div>
</div>
<div dir="ltr">
<div><span style="font-size: 12.8px;"><span style="background-color: rgba;"><strong>Título</strong>: </span></span><span style="font-size: 12.8px;">Nonlocal evolution equations</span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;"><br /></span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;"><strong>Resumen</strong>: (Versión pdf <a href="http://www.mate.unlp.edu.ar/coloquiodm/abstracts/rossi.pdf">aquí</a>)</span></span></div>
<div style="font-size: 12.8px;">We study the fractional <img id="l0.9029844305202506" class="va_li" style="display: inline; vertical-align: -2.934px;" title="p-" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09p-" alt="p-" width="20" height="10" />Laplacian evolution</div>
<div style="font-size: 12.8px;">equation given by </div>
<div style="font-size: 12.8px;">$$u_t (t,x)=\int_{A}</div>
<div style="font-size: 12.8px;">\frac{1}{\vert x - y \vert^{N+sp}}|u (t,y)-u(t,x)|^{p-2}(u (t,y)-u(t,x)) dy\qquad\hbox{for</div>
<div style="font-size: 12.8px;"><img id="l0.7547010662585569" class="va_li" style="display: inline; vertical-align: -0.367px;" title="x\in\Omega" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09x%5Cin%5COmega" alt="x\in\Omega" width="40" height="12" />, <img id="l0.9478214641974976" class="va_li" style="display: inline; vertical-align: -0.367px;" title="t>0" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09t>0" alt="t>0" width="35" height="12" />},$$</div>
<div style="font-size: 12.8px;"><img id="l0.8014726181285114" class="va_li" style="display: inline; vertical-align: -0.367px;" title="0<s<1" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%090<s<1" alt="0<s<1" width="67" height="12" />, <img id="l0.0741247709457955" class="va_li" style="display: inline; vertical-align: -2.934px;" title="p\ge 1" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09p%5Cge%091" alt="p\ge 1" width="38" height="14" />.</div>
<div style="font-size: 12.8px;">In a bounded domain <img id="l0.8104614089492113" class="va_li" style="display: inline;" title="\Omega" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09%5COmega" alt="\Omega" width="10" height="11" /> we deal with the Dirichlet problem by taking <img id="l0.8636898867933598" class="va_li" style="display: inline;" title="A=\mathbb{R}^N" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09A=%5Cmathbb{R}%5EN" alt="A=\mathbb{R}^N" width="57" height="14" /> and <img id="l0.9761598176318274" class="va_li" style="display: inline;" title="u=0" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09u=0" alt="u=0" width="38" height="11" /> in <img id="l0.20011711459985504" class="va_li" style="display: inline; vertical-align: -3.667px;" title="\mathbb{R}^N\setminus \Omega" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09%5Cmathbb{R}%5EN%5Csetminus%09%5COmega" alt="\mathbb{R}^N\setminus \Omega" width="51" height="18" />, and the Neumann problem by taking <img id="l0.1654710180369594" class="va_li" style="display: inline;" title="A=\Omega" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09A=%5COmega" alt="A=\Omega" width="45" height="12" />.</div>
<div style="font-size: 12.8px;">We include here the limit case <img id="l0.9836101190851834" class="va_li" style="display: inline; vertical-align: -2.934px;" title="p=1" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09p=1" alt="p=1" width="38" height="14" /> that has the extra difficulty of giving a meaning to $\frac{ u(y) - u(x)}{\vert u(y) - u(x) \vert} $ when <img id="l0.3058748908762978" class="va_li" style="display: inline; vertical-align: -3.667px;" title="u(y)=u(x)" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09u(y)=u(x)" alt="u(y)=u(x)" width="83" height="16" />.</div>
<div style="font-size: 12.8px;">We also consider the Cauchy problem in the whole <img id="l0.999386232592905" class="va_li" style="display: inline;" title="\mathbb{R}^N" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09%5Cmathbb{R}%5EN" alt="\mathbb{R}^N" width="23" height="14" /> by taking <img id="l0.12341506273155112" class="va_li" style="display: inline;" title="A=\Omega=\mathbb{R}^N" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09A=%5COmega=%5Cmathbb{R}%5EN" alt="A=\Omega=\mathbb{R}^N" width="92" height="14" />.</div>
<div style="font-size: 12.8px;">We find existence and uniqueness of strong solutions for each of the above mentioned problems. We also study the asymptotic behaviour of these solutions as <img id="l0.5165321978401549" class="va_li" style="display: inline;" title="t \to \infty" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09t%09%5Cto%09%5Cinfty" alt="t \to \infty" width="47" height="11" />. Finally, we recover the local <img id="l0.7400848048105084" class="va_li" style="display: inline; vertical-align: -2.934px;" title="p-" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09p-" alt="p-" width="20" height="10" />Laplacian evolution equation with Dirichlet or Neumann boundary conditions, and for the Cauchy problem, by taking the limit as <img id="l0.06826497797258702" class="va_li" style="display: inline;" title="s \to 1" src="https://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09s%09%5Cto%091" alt="s \to 1" width="39" height="11" /> in the nonlocal problems multiplied by a suitable scaling constant.</div>
<br />
<div style="font-size: 12.8px;"> </div>
</div>
<div style="font-size: 12.8px;" dir="ltr"><span style="font-size: small;"><span style="background-color: rgba;"><br /></span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;">Están invitados a participar!<br /></span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;"><br /></span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;">Para más información <span>del</span> <span>coloquio</span>, visitar la página web <a href="http://www.mate.unlp.edu.ar/coloquiodm/">aquí</a></span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;"><span style="background-color: rgba;"><br /></span></span></div>
<div style="font-size: 12.8px;"><span style="font-size: small;">Saludos,<br />Gastón</span></div>
</div>
</div>
</div>
<div> </div>
</body></html>