54 research outputs found
Study of solutions to an initial and boundary value problem for certain systems with variable exponents
Existence,uniqueness, and nonexistence of solutions to nonlinear diffusion equations with p ( x , t ) -Laplacian operator
Evolution problems of Navier-Stokes type with anisotropic diffusion
In this work, we consider the evolutive problem for the incompressible Navier-Stokes equations with a general diffusion which can be fully anisotropic. The existence of weak solutions is proved for the associated initial problem supplemented with no-slip boundary conditions. We prove also the properties of extinction in a finite time, exponential time decay and power time decay. With this respect, we consider the important case of a forces fields with possible different behavior in distinct directions. Perturbations of the asymptotically stable equilibrium are established as well
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