We consider a quasi-linear parabolic (possibly, degenerate) equation with nonlinear
dynamic boundary conditions. The corresponding class of initial and boundary value …

In this study, we investigate reaction-diffusion and elliptic-like equations with two classes of
dynamic boundary conditions, of reactive and reactive-diffusive type. We provide sharp …

In this paper, we consider a class of coupled systems of PDEs, denoted by (ACE) ε for ε≥ 0.
For each ε≥ 0, the system (ACE) ε consists of an Allen–Cahn type equation in a bounded …

The existence of a unique minimal pullback attractor is established for the evolutionary
process associated with a non-autonomous quasi-linear parabolic equations with a …

The Allen–Cahn equation, coupled with dynamic boundary conditions, has recently received
a good deal of attention. The new issue of this paper is the setting of a rather general mass …

This article focuses on investigating the null controllability of a volume-surface reaction-
diffusion equation with dynamic boundary conditions. Notably, the reaction and diffusion …

In this paper, we study the long-time behavior of the reaction–diffusion equation with
dynamical boundary condition, where the nonlinear terms f and g satisfy the polynomial …

We present a new formulation and generalization of the classical theory of heat conduction
with or without fading memory. As a special case, we investigate the well-posedness of …

In this paper, we derive optimal upper and lower bounds on the dimension of the attractor
A_W for scalar reaction–diffusion equations with a Wentzell (dynamic) boundary condition …

We investigate classical solutions of nonlinear elliptic equations with two classes of
dynamical boundary conditions, of reactive and reactive–diffusive type. In the latter case it is …