<div dir="ltr"><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000">Dear all,</font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000">as a part of the series of seminars <i>"Insalate di Matematica"</i>, we remind you that today there is a seminar held by <b>Noemi David</b> (Laboratoire Jacques-Louis Lions - Sorbonne Université). The talk will be held online and it will also be broadcast in room 3014 (building U5-Ratio, Università degli Studi di Milano-Bicocca) by prior reservation at the link <a href="https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0" target="_blank">https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0</a></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000">You will be required to exhibit your Covid certification at the entrance of the building.</font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000">Here the details:</font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000"><span style="text-decoration-line:underline">Speaker</span>: <b>Noemi David (Laboratoire Jacques-Louis Lions - Sorbonne Université)</b></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000"><span style="text-decoration-line:underline">Date and time</span>: <b>7th April 2022, 2:00 pm (CET)</b></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000"><span style="text-decoration-line:underline">Title</span>: <i>"On the incompressible limit for tumor growth models including nutrients and convective effects"</i></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000"><span style="text-decoration-line:underline">Webex link</span>: <a href="https://unimib.webex.com/unimib/j.php?MTID=mbbd40f861fa4038a8cda07ffd618fb2c" target="_blank">https://unimib.webex.com/unimib/j.php?MTID=mbbd40f861fa4038a8cda07ffd618fb2c</a><span style="text-decoration-line:underline"> </span>(<span style="text-decoration-line:underline"><i>Password</i></span>: Insalate)</font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000"><span style="text-decoration-line:underline">Abstract</span>: Both compressible and incompressible porous medium models are used in the literature to describe the mechanical properties of living tissues. Relying on Darcy's law, these models describe the tendency of tumor cells to move down pressure gradients, away from highly congested regions. These two different representations can be related using a stiff pressure law. In the incompressible limit, the compressible model generates a free boundary problem of Hele-Shaw type where the cell density is saturated. In this talk, I will discuss the analysis of the incompressible limit of a model including the effect of a nutrient (or possibly an external drift). The main difficulty is to deduce the pressure equation in the limit. To this end, we prove the strong compactness of the pressure gradient, blending two techniques: an extension of the usual Aronson-Bénilan estimate in an <img alt="L^2" title="L^2" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=L%5E2" id="gmail-m_-3430815051550445128gmail-m_-3893873976392164144m_-5434215198406858321m_8002150859588060076gmail-l0.41832918026007904" width="15" height="13" style="display: inline;">-setting, and a sharp <img alt="L^4" title="L^4" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=L%5E4" id="gmail-m_-3430815051550445128gmail-m_-3893873976392164144m_-5434215198406858321m_8002150859588060076gmail-l0.6107467195741421" width="15" height="13" style="display: inline;">-uniform bound of the pressure gradient.</font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000"><span style="text-decoration-line:underline">Keywords</span>: Porous medium equation - Incompressible limit - Free boundary - Hele-Shaw - Tumor growth.</font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000"><b><i>** We inform you that the talk will be recorded and uploaded on our website. If you join the talk </i></b><span style="text-decoration-line:underline"><b><i>after the starting time</i></b></span><b><i>, we kindly ask you to ensure that </i></b><span style="text-decoration-line:underline"><b><i>your microphone and webcam are turned off</i></b></span><b><i> **</i></b></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" target="_blank">insalate.matematica@unimib.it</a>.</font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000"><br></font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000"><br></font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><span style="color:rgb(0,0,0);font-family:arial,sans-serif">We are looking forward to seeing you!</span><font face="arial, sans-serif" color="#000000"><br></font></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal;min-height:15px"><br></p>
<p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif" color="#000000">The organizers: Luigi Appolloni, Andrea Bisterzo, Alberto Cassella, Francesca Cottini, Ludovico Marini</font></p></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Il giorno lun 4 apr 2022 alle ore 14:45 Mbs Insalate Di Matematica <<a href="mailto:insalate.matematica@unimib.it">insalate.matematica@unimib.it</a>> ha scritto:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">
<div dir="ltr"><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">As part of the series of seminars <i>"Insalate di Matematica"</i>, <b>Noemi David</b>, PhD student at <span style="word-spacing:0px">the</span><span style="font-weight:normal"><span> Laboratoire Jacques-Louis Lions - Sorbonne Université</span></span><font style="word-spacing:0px"><span style="word-spacing:1px">, will deliver a talk. </span></font></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">
The seminar will be held online and, according to the current Covid regulations, it will also be broadcast in room 3014 <b>(more information below)</b>
</font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">Here the details:</font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><u>Date and time</u>: <b>7th April 2022, 2:00 pm (CET)</b></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><u><br></u></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><u>Title</u>: <i style="background-color:rgb(241,194,50)">"<span>On the incompressible limit for tumor growth models including nutrients and convective effects</span></i><span style="background-color:rgb(241,194,50)"><i>"</i></span><i><br><span style="background-color:rgb(241,194,50)"></span></i></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div dir="ltr"><span style="color:rgb(0,0,0)"><font size="2"><u style="word-spacing:1px">Abstract</u><span style="word-spacing:1px">:</span>
<span style="font-family:Arial,Helvetica,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none">Both compressible and incompressible porous medium models are used in the literature to describe the mechanical properties of living tissues. Relying on Darcy's law, these models describe the tendency of tumor cells to move down pressure gradients, away from highly congested regions. These two different representations can be related using a stiff pressure law. In the incompressible limit, the compressible model generates a free boundary problem of Hele-Shaw type where the cell density is saturated. In this talk, I will discuss the analysis of the incompressible limit of a model including the effect of a nutrient (or possibly an external drift). The main difficulty is to deduce the pressure equation in the limit. To this end, we prove the strong compactness of the pressure gradient, blending two techniques: an extension of the usual Aronson-Bénilan estimate in an<span> </span></span><img alt="L^2" title="L^2" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=L%5E2" id="gmail-m_6738734633195848593m_-5434215198406858321m_8002150859588060076gmail-l0.41832918026007904" style="font-family: Arial, Helvetica, sans-serif; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: inline;" width="15" height="13"><span style="font-family:Arial,Helvetica,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none">-setting, and a sharp<span> </span></span><img alt="L^4" title="L^4" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=L%5E4" id="gmail-m_6738734633195848593m_-5434215198406858321m_8002150859588060076gmail-l0.6107467195741421" style="font-family: Arial, Helvetica, sans-serif; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: inline;" width="15" height="13"><span style="font-family:Arial,Helvetica,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;display:inline;float:none">-uniform bound of the pressure gradient.</span>
<br><br></font></span></div><div dir="ltr"><span style="color:rgb(0,0,0)"><font size="2"><span style="font-family:Roboto,-apple-system,BlinkMacSystemFont,"Apple Color Emoji","Helvetica Neue",sans-serif"></span></font></span></div><div dir="ltr"><div dir="auto"><span style="color:rgb(0,0,0)"><font size="2"><u style="word-spacing:1px">Keywords</u><span style="word-spacing:1px">:
Porous medium equation - Incompressible limit - Free boundary - Hele-Shaw - Tumor growth.
</span></font></span><div><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div>
</div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div>
<div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><b><u>Information to attend in room 3014<br></u></b></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">The
seminar will also be broadcast in room 3014, at the building U5-Ratio,
Università degli Studi di Milano Bicocca. For the traceability of
persons present in the department, reservation is mandatory. You can reserve at the following link: <a href="https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0" target="_blank">https://sites.google.com/view/insalate-di-matematica/reservation?authuser=0</a></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">We also remind that you will be required to exhibit your green pass at the entrance of the building.</font></span></div>
<div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><b><u>Information to attend online</u></b></font></span></div><div style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">The seminar will be streamed via Webex platform at the following link: <a href="https://unimib.webex.com/unimib/j.php?MTID=mbbd40f861fa4038a8cda07ffd618fb2c" target="_blank">https://unimib.webex.com/unimib/j.php?MTID=mbbd40f861fa4038a8cda07ffd618fb2c</a>
(<i><u>Password</u></i>: Insalate)<br></font></span></div><div dir="auto"><span style="color:rgb(0,0,0)"><font size="2"><i><b>** We inform you that the talk will be recorded and uploaded on our website. If you join the talk <u>after the starting time</u>, we kindly ask you to ensure that <u>your microphone and webcam are turned off</u> **</b></i><br></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">You can find the poster of the event in the attachment. We are looking forward to seeing you! </font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" target="_blank">insalate.matematica@unimib.it</a>.</font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br></font></span></div><div dir="auto" style="word-spacing:1px"><span style="color:rgb(0,0,0)"><font size="2"><br>The organizers: Luigi Appolloni, Andrea Bisterzo, Alberto Cassella, Francesca Cottini, Ludovico Marini</font></span></div></div></div>
</div>
</blockquote></div>