@Article{CAM-19-21,
author = {},
title = {【短期课程】An Introduction to Stochastic Scalar Conservation Laws, 2022-10-31},
journal = {CAM-Net Digest},
year = {2022},
volume = {19},
number = {21},
pages = {5--5},
abstract = {<p style="text-align: justify;">Time: 2022-10-31 19:00 — 21:00<br/>Venue: 腾讯会议<br/>Speaker: Hermano Frid<br/>Affiliation: Instituto de Matematica Pura e Aplicada-IMPA, Brazil<br/>Tencent Meeting ID: 463 9509 7151<br/>Meeting Password: 1234&nbsp;<a href="https://meeting.tencent.com/dm/RpAX62WD3oM6">https://meeting.tencent.com/dm/RpAX62WD3oM6</a></p><p style="text-align: justify;">Abstract:<br/>This mini-course will contain the following:</p><p style="text-align: justify;">1) Deterministic scalar conservation laws. The example of the Burgers equation and the non-existence of a global&nbsp;smooth solution. Definition of weak solution. Non-uniqueness. The concept of entropy solution. Young measures.&nbsp;Measure-valued solutions. Existence and $L^1$ stability of bounded entropy solutions. Kinetic formulation. Kinetic&nbsp;defect measure. The concept of kinetic solution. Example of the Burgers equation.&nbsp;</p><p style="text-align: justify;">2) Stochastic conservation laws. A primer in Stochastic integration. Itô&#39;s formula. Kinetic formulation. Generalized&nbsp;kinetic solution. Energy estimate. Estimate of the kinetic measures. Estimate of the Young measures. Doubling of&nbsp;variables. $L^1$ contraction. Overview of invariant measures of stochastic conservation laws.</p><p style="text-align: justify;">References:<br/>[DPZ] G. Da Prato, J. Zabczyk. &quot;Stochastic Equations in Infinite Dimensions&#39;&#39;. Encyclopedia Math. Appl., vol. 44,&nbsp;Cambridge University Press, Cambridge. 2nd Edition 2014.<br/>[DV] A. Debussche, J. Vovelle. Scalar conservation laws with stochastic forcing. J. Funct. Anal. 259 (2010) 1014-1042.<br/>[DV2] A. Debussche, J. Vovelle. Invariant measures of scalar first-order conservation laws with stochastic&nbsp; forcing.&nbsp;Probab. Theory Relat. Fields (2015) 163, 575-611.<br/>[Kr] S.N. Kruzhkov. First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81 (123)&nbsp;(1970) 228-255.<br/>[Pe] B. Perthame. &quot;Kinetic Formulation of Conservation Laws&#39;&#39;. Oxford Lecture Ser. Math. Appl. Vol. 21,&nbsp;Oxford University Press, Oxford, 2002.<br/>[FLMNZ] H. Frid, Y. Li, D. Marroquin, J.F. Nariyoshi and Z. Zeng. The Strong Trace Property and&nbsp; the Neumann&nbsp;Problem for Stochastic Conservation Laws. Stochastic Partial Differential Equations: Analysis and Computations,&nbsp;Published online, 2021.</p>},
issn = {},
doi = {https://doi.org/2022-CAM-21188},
url = {https://global-sci.com/article/74984/an-introduction-to-stochastic-scalar-conservation-laws-2022-10-31}
}