Front propagation is a ubiquitous phenomenon. It arises in physical, biological and cross-disciplinary systems as diverse as flame propagation, superconductors, virus infections, cancer spread or transitions in human prehistory. Here we derive a single, approximate front speed from three rather...

This work is concerned with a class of semilinear stochastic functional parabolic differential equations of retarded type. We first establish conditions to ensure the existence of a unique non-negative solution of the stochastic delay partial differential equation under investigation....

To bridge the structure gap, electrochemical reactions can be studied in flow cells with nm-sized catalyst particles deposited or fabricated on the cell walls. The understanding of the role of mass transport in such cells is now limited. To clarify the likely effects in this field, we analyze...

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be approximated from prior measurements of wildfires. An...

We investigate pattern formation in a fractional reaction–diffusion system. By the method of computer simulation of the model of excitable media with cubic nonlinearity we are able to show structure formation in the system with time and space fractional derivatives. We further compare the...

This paper is concerned with the Murray–Thomas model for interacting chemicals or species, under Robin boundary data. It is shown that the solutions are bounded and asymptotically converging toward an absorbing set of the phase-space. The stability of the positive constant steady states is...

We consider a model introduced recently [Nature 424(2003)900], for describing competition between two languages, which in typical situations predicts the extinction of one of them. We generalize it by introducing a spatial dependence in terms of a reaction–diffusion equation. We show that in...