[CvGmt News] Seminario di Philippe Souplet (15 maggio 2018, ore 14:30)

Alfonso Sorrentino sorrentino at mat.uniroma2.it
Wed May 9 07:26:42 CEST 2018


SEMINARIO DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Universita' degli Studi di Roma "Tor Vergata"



Martedi' 15 Maggio 2018, ore 14:30 Aula Dal Passo

Philippe Souplet (Université Paris XIII)


Titolo: Reaction-diffusion systems with dissipation of mass: old and new
results.


Abstract: We consider positivity-preserving reaction-diffusion systems of
the form

$$\partial_t u_i-d_i\Delta d_i=f_i(u),\qquad u=(u_1,\dots,u_m),$$

under the Neumann boundary conditions, with the structure condition $\sum
f_i\le 0$, which guarantees that the total mass is nonincreasing in time.
Such systems are often encountered in applications, for instance in models
of reversible chemistry.

Whereas global existence and boundedness of solutions is easy in the
equidiffusive case $d_i\equiv d$,  the question becomes quite involved in
the case when the $d_i>0$ are different
(a case which is indeed relevant in models of chemical reactions), and
there has been an abundant mathematical literature on this question in the
past 30 years.

Various sufficient conditions on the nonlinearities $f_i$ for global
existence are known, as well as examples of finite time blow-up for certain
systems. The latter is a special case of the so-called diffusion induced
blow-up phenomenon.

We will discuss old and new results on this subject.



Website: http://www.mat.uniroma2.it/~sorrenti/SeminarioED.html




-- 
Dipartimento di Matematica
Università degli Studi di Roma "Tor Vergata"
Via della Ricerca Scientifica 1
00133 Rome (Italy)

Phone: +39 06 72594663
Fax:      +39 06 72594699
Web page: http://www.mat.uniroma2.it/~sorrenti
Email: sorrentino at mat.uniroma2.it
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