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We first prove an abstract result for a class of nonlocal
problems using fixed point method. We apply this result to
equations revelant from plasma physic problems. These equations
contain terms like monotone or relative rearrangement of functions.
So, we start the approximation study by using finite element to
discretize this nonstandard quantities. We end the paper by giving
a numerical resolution of a model containing those terms.
We propose a modification of the classical Boussinesq approximation for buoyancy-driven flows of viscous, incompressible fluids in situations where viscous heating cannot be neglected. This modification is motivated by unresolved issues regarding the global solvability of the original system. A very simple model problem leads to a coupled system of two parabolic equations with a source term involving the square of the gradient of one of the unknowns. Based on adequate notions of weak and strong...
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