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题目: On evolutionary problems with a-priori bounded gradient


报告人:Prof. Josef Malek, Charles Univaersity in Prague


摘要: We  study nonlinear  evolutionary  partial  differential  equations that can be  viewed  as  a  generalization  of  the  heat  equation  where  the temperature  gradient is a priori bounded  but  the  heat  flux  has merely linear growth. We use the concept of renormalized solution and higher  differentiability  techniques  to  prove  the existence and uniqueness of weak solution with L^1-integrable heat-flux for all values of the material parameters.  Under some more restrictive assumptions on the material paramter, we prove higher integrability of the heat flux. This is a joint work with Miroslav Bulíček and David Hruška. Some key ideas of the approach comes from the result concerning analysis of nonlinear solids with bounded linearized strain presented in the paper: Beck, L., Bulicek, M., Malek, J., Suli, E.: On the existence of integrable solutions to nonlinear elliptic systems and variational problems with linear growth. Arch. Ration. Mech. Anal. 225 (2017) 717–769. The relation to fluid mechanics problems will be also shown.


时间:2019年9月5日  15:00-16:00


地点:西大楼 308


邀请人:吕勇 老师