Differentiability of measure solutions to the nonlinear transport equation

Speaker(s)

Kamila Łyczek

Affiliation

doktorantka MIM

Date

May 30, 2019, 12:30 p.m.

Room

room 5070

Seminar

Seminar of Mathematical Physics Equations Group

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We consider the nonlinear transport equation in the space of bounded Radon measures. Previous results concerning this type of equation include well-posedness and Lipschitz dependence of the solution (on the initial condition and model ingredients). However, these results do not allow to analyze the differentiability of solutions with respect to a perturbation of the system. Thus, a new setting is necessary. We have shown that solutions are differentiable with respect to the perturbing parameter in a proper space, which is predual to (C^{1+\alpha}). The knowledge of differentiability is necessary for various applications, e.g. in the optimal control theory.

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