The present review summarizes experimental and theoretical work dealing with self-
organized solitary localized structures (LSs) that are observed in spatially extended …

If we had to formulate in one sentence what this book is about, it might be “How partial
differential equations can help to understand heat explosion, tumor growth or evolution of …

This paper deals with the existence of travelling wave fronts in reaction–diffusion systems
with spatio-temporal delays. Our approach is to use monotone iterations and a nonstandard …

Nonlocal reaction–diffusion equations describe various biological and biomedical
applications. Their mathematical properties are essentially different in comparison with the …

In this paper we consider a mathematical model of cancer cell invasion of tissue
(extracellular matrix). Two crucial components of tissue invasion are (i) cancer cell …

Spatio-temporal pattern formation in reaction–diffusion models of interacting populations is
an active area of research due to various ecological aspects. Instability of homogeneous …

In this paper, we study the effect of spatial average and time delay on the dynamics of a
diffusive predator–prey model under the Neumann boundary condition. Compared to the …

This paper is concerned with the diffusive Nicholson's blowflies model with nonlocal (or
spatiotemporal) delay. When the spatial variable is one-dimensional, we establish the …

A diffusive Lotka–Volterra competition model with nonlocal intraspecific and interspecific
competition between species is formulated and analyzed. The nonlocal competition strength …

This paper is concerned with the calculation of the normal form on the center manifold up to
the third-order term at the double-Hopf singularity for general partial functional differential …