Nonlinear distributions and quasilinear ellipticity

Nonlinear Stability for Dissipative Nonlinear Evolution Equations with Ellipticity

We study the Cauchy problem for a set of nonlinear evolution equations, which has been proposed for the investigation of nonlinear interaction between ellipticity and dissipation. The zero equilibrium is linearly stable for coeecients within certain range. We further establish the global existence, nonlinear stability and optimal decay rate of the solution for coeecients within the same range, ...

Nonlinear Transmission Problems for Quasilinear Parabolic Systems

We study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions.

Quasilinear Elliptic Systems of Resonant Type and Nonlinear Eigenvalue Problems

Quantifying the Cosmic Web I: The large-scale halo ellipticity-ellipticity and ellipticity-direction correlations

The formation of dark matter halos tends to occur anisotropically along the filaments of the Cosmic Web, which induces both ellipticity-ellipticity (EE) correlations between the shapes of halos, as well as ellipticity-direction (ED) cross-correlations between halo shapes and the directions to neighboring halos. We analyze the halo catalogue and the semi-analytic galaxy catalogue of the recent M...

Ellipticity and Ergodicity

Let S = {St}t≥0 be the submarkovian semigroup on L2(R ) generated by a self-adjoint, second-order, divergence-form, elliptic operator H with Lipschitz continuous coefficients cij . Further let Ω be an open subset of R . We prove that S leaves L2(Ω) invariant if, and only if, it is invariant under the flows generated by the vector fields Yi = ∑d j=1 cij∂j .