In this paper, we review several results from singularly perturbed differential equations with
multiple small parameters. In addition, we develop a general conceptual framework to …

Numerical continuation and bifurcation methods can be used to explore the set of steady
and time–periodic solutions of parameter dependent nonlinear ODEs or PDEs. For PDEs, a …

A focused summary of one-and two-dimensional models for linear and nonlinear wave
propagation in fractional media is given. The basic models, which represent fractional …

The concept of Turing instability, namely that diffusion can destabilize the homogenous
steady state, is well known either in the context of partial differential equations (PDEs) or in …

This paper studies the Lotka-Volterra competition model with cross-diffusion terms under
homogeneous Dirichlet boundary conditions. We consider the asymptotic behavior of …

Partial differential equations (PDEs) involving fractional Laplace operators have been
increasingly used to model non-local diffusion processes and are actively investigated using …

In this paper, we consider the Shigesada-Kawasaki-Teramoto (SKT) model, which presents
cross-diffusion terms describing competition pressure effects. Even though the reaction part …

In this paper we investigate the bifurcation structure of the cross-diffusion Shigesada–
Kawasaki–Teramoto model (SKT) in the triangular form and in the weak competition regime …

We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a
cross-diffusion system at the fast reaction limit. The system models a competition of two …

In the last three decades, powerful computer-assisted techniques have been developed in
order to validate a posteriori numerical solutions of semilinear elliptic problems of the form Δ …