Nonlinear Diffusion Equations

Abstract

Newtonian filtration equations: existence and uniqueness of solutions - one dimensional case existence and uniqueness of solutions - higher dimensional case regularity of solutions - one dimensional case regularity of solutions - higher dimensional case properties of the free boundary - one dimensional case properties of the free boundary - higher dimensional case initial trace of solutions other problems. Non-Newtonian filtration equations: existence of solutions Harnack inequality and initial trace of solutions regularity of solutions uniqueness of solutions properties of the free boundary other problems. General quasilinear equations of second order: weakly degenerate equations in one dimension weakly degenerate equations in higher dimension strongly degenerate equations in one dimension degenerate equations in higher dimension without terms of lower order general strongly degenerate equations in higher dimension classes BV and BV. Nonlinear diffusion equations of higher order: similarity solutions of a fourth order equation equations with double-degeneracy Cahn-Hilliard equation with constant mobility Cahn-Hilliard equations with positive concentration dependent mobility thin film equation Cahn-Hilliard equation with degenerate mobility.