The space BV of functions of bounded variation is not enough for hyperbolic conservation laws
Prof. Stéphane Junca,
University of Nice Sophia Antipolis, Nice (UNS)
| Speaker |
Prof. Stéphane Junca,
University of Nice Sophia Antipolis, Nice (UNS)
|
|---|---|
| When |
Feb 07, 2020
from 10:00 AM to 11:00 AM |
| Where | LH 006 |
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Abstract : In 1983 K.S. Cheng published an article with this title. He built some entropy solutions which do not belong to BV. Later, in 1994, Lions, Perthame and Tadmor proved a reguralized effect of solutions for nonlinear scalar conservation laws in Sobolev spaces but not in BV. Fractional BV spaces \(BV^s\), 0 < s < 1, seem to be a natural response to K.S. Cheng on BV. They are well designed to capture the structure of shock waves. As first applications, the stability and the optimal smoothing effect in \(BV^s\) for entropy solutions with some numerical schemes are presented.