engleski

Nonlinear diffusive equations of higher order

Nonlinear diffusion equations of fourth and higher order have been of interest in various fields of mathematical physics. Application range from fluid models for thin viscous films to statistical equations for quantum particles. Here we consider the fourth-order {; ; \sl Derrida-Lebowitz-Speer-Spohn (DLSS) equation}; ; and sixth-order nonlinear parabolic equation. For DLSS equation we introduce a numerical method based on a Wasserstein gradient flow. For the sixth-order equation we prove the global-in-time existence of weak nonnegative solutions in one space dimension with periodic boundary conditions.

Higher-order diffusive equations; numerical solution; Wasserstein gradient flow; global existence of periodic solutions; algorithmic entropy construction; entropy dissipation; long-time behavior of the solutions

nije evidentirano