Numerical approximations of the relative rearrangement : the piecewise linear case. Application to some nonlocal problems
Relative rearrangement on a finite measure space. Application to the regularity of weighted monotone rearrangement (Part I)
Relative rearrangement on a finite measure space. Application to weighted spaces and to P.D.E.
Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems
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.
A parabolic system involving a quadratic gradient term related to the Boussinesq approximation.
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...
Trace imbeddings for -sets and application to Neumann-Dirichlet problems with measures included in the boundary data
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