9月5日：On evolutionary problems with a-priori bounded gradient
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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.