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80-XX Classical thermodynamics, heat transfer
80Mxx Basic methods

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Entropy solutions for parabolic equations in Musielak framework without sign condition and with measure data

M.S.B. Elemine Vall, A. Ahmed, A. Touzani, Abdelmoujib Benkirane (2020)

Archivum Mathematicum

We prove an existence result of entropy solutions for a class of strongly nonlinear parabolic problems in Musielak-Sobolev spaces, without using the sign condition on the nonlinearities and with measure data.

Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems

Pedro Merino, Ira Neitzel, Fredi Tröltzsch (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.

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