On global solutions for quasilinear one-dimensional parabolic problems with dynamical boundary conditions

Abstract

We provide sufficient and almost optimal conditions for global existence of classical solutions in parabolic Hölder spaces to quasilinear one-dimensional parabolic problems with dynamical boundary conditions.Date: May 4, 2015. Key words and phrases. Dynamical boundary conditions, global solutions, Bernstein-Nagumo condition, doubling of variables. 1 Here and in the following, equations at the boundary points x = ±ℓ as (1.2) involving ± signs (or ∓ signs) are to be understood as two equations with a + sign (or − sign) at x = +ℓ and a − sign (or + sign) at x = −ℓ. The sign convention is chosen such that ±ux(±ℓ) represents the "outward" normal derivative.