Conservation laws in heterogeneous media

Abstract

<p>Doktorska disertacija posve&para;cena je re&middot;savanju nelinearnih hiperboli&middot;cnih skalarnih zakona odr&middot;zanja u heterogenim sredinama, prou&middot;cavanjem osobina kompaktnosti re&middot;senja familija aproksimativnih jedna&middot;cina. Ta&middot;cnije, u cilju dobijanja re&middot;senja u = u(t; x) problema @ t u + divx f (t; x; u) = 0;uj t=0 = u 0(x); gde su promenljive x 2 R d i t 2 R+<br />, posmatramo familije problema koji na neki na&middot;cin aproksimiraju po&middot;cetni problem, a koje znamo da re&middot;simo, i ispitujemo familije dobijenih re&middot;senja koja zovemo aproksimativna re&middot;senja. Cilj nam je da poka&middot;zemo da je dobijena familija u nekom smislu prekompaktna,<br />tj. da ima konvergentan podniz &middot;cija granica re&middot;sava po&middot;cetni problem.</p>

<p>Doctoral theses is dedicated to solving nonlinear hyperbolic scalar conservation laws in heterogeneous media, by studying compactness properties of the family of solutions to approximate problems. More precise, in order to obtain solution u = u(t; x) to the problem @ t u + divx f (t; x; u) = 0; uj t=0 = u 0 (x); (4.18) where x 2 R d and t 2 R+<br />, we study the solutions of the families of problems that, in some way, approximate previously mentioned problem, which we know how to solve. We call those solutions approximate solutions. The aim is to show that the obtained family is in some sense precompact, i.e. has convergent subsequence that solves the problem (4.18).</p>