On the Dynamics of a Class of Partial Differential Equations

We study the dynamical behavior of a class of partial differential equations which includes the transport equation with decay, the advection-diffusion with decay, the linearized KdV equation and the linearized BBM equation. We characterize the stability regions as well as the chaotic regions in terms of the coefficients of the equation and the weight of the Herzog space. Consequently, we will obtain relations between the chaotic and unstable regions, finding out that under certain restrictions both coincide. © 2024 Elsevier Inc.