Existence proofs for pseudomonotone parabolic problems

Abstract: In the talk we discuss nonlinear parabolic problems which contain a pseudomonotone operator. A new notion of Bochner pseudomonotonicity is introduced and applied. Extensions to quasi non-conforming and non-conforming Bochner pseudomonotonicity yield convergence proofs for fully discrete Rothe–Galerkin schemes in the framework of discretely divergence free FE and DG methods.

References [1] E. Baumle and M. Růžička: Note on the existence theory for evolution equations with pseudomonotone operators, Ric. Mat., 2017.

[2] S. Bartels, M. Růžička: Convergence of fully discrete implicit and semi-implicit approximations of singular parabolic equations, SIAM J. Numer. Anal., 2020.

[3] A. Kaltenbach, M. Růžička: Note on the existence theory for pseudo-monotone evolution problems, J. Evol. Equ., 2021.

[4] L.C. Berselli, A. Kaltenbach, M. Růžička: Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications, Math. Models Methods Appl. Sci., 2021.

[5] A. Kaltenbach, M. Růžička: Analysis of fully discrete, non-conforming approximation of evolution equations and applications, in preparation, 2022.

MathematicsPhysics

Audience: researchers in the topic

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).

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