In this work, we study the propagation of wildfires using an advection--diffusion--reaction
model which also includes convective and radiative heat loss. An existing model is …

We analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems that arise, for
example, in the modelling of biofilm growth. One of the equations, describing the evolution of …

We propose a new mathematical framework for the addition of stochastic attachment to
biofilm models via the use of random ordinary differential equations. We focus our approach …

We present the stability analysis of two free boundary problems arising in biofilm modelling.
The first, introduced in the 1980s by Wanner and Gujer, is related to the competition …

We study the existence and the longterm behavior of solutions of a parabolic equation
governed by the p-Laplacian with nonlinear growth terms that are coupled with the solutions …

We investigate traveling wave solutions for a nonlinear system of two coupled reaction-
diffusion equations characterized by double degenerate diffusivity:\[n_t=-f (n, b),\quad b_t=[g …

Motivated by models for biofilm growth, we consider Cauchy problems for quasilinear
reaction diffusion equations where the diffusion coefficient has a porous medium type …

In my research I studied differential equations, which are ubiquitous in science and
engineering. The equation I investigated has an application in biofilm modelling. These are …