Wave bifurcation in models for heterogeneous catalysis.
Wave of Chaos and Pattern Formation in Spatial Predator-Prey Systems with Holling Type IV Predator Response
The challenges to live in the open water and the diversity of habitats in the marine environments prompts phytoplankton to devise strategies which often involve production of toxins by Harmful Algal Bloom (HAB) and rapid production of metabolites from non-toxic precursor. The functional response of the predator is described by Holling type IV. We investigate wave phenomena and non-linear non-equilibrium pattern formation in a phytoplankton-zooplankton system with Holling type IV functional response....
Waves of Autocrine Signaling in Patterned Epithelia
A biophysical model describing long-range cell-to-cell communication by a diffusible signal mediated by autocrine loops in developing epithelia in the presence of a morphogenetic pre-pattern is introduced. Under a number of approximations, the model reduces to a particular kind of bistable reaction-diffusion equation with strong heterogeneity. In the case of the heterogeneity in the form of a long strip a detailed analysis of signal propagation is...
Waves of excitations in heterogeneous annular region, asymmetric arrangement
This paper deals with the propagation of waves around a circular obstacle. The medium is heterogeneous: the velocity is smaller in the inner region and greater in the outer region. The interface separating the two regions is also circular, and the obstacle is located eccentrically inside it. The different front portraits are classified.
Weak- solutions for a model of self-gravitating particles with an external potential
The existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential is studied in weak- spaces (i.e. Markiewicz spaces). The main goal is to prove the existence of global solutions and to study their large time behaviour.
Weak periodic solutions of some quasilinear parabolic equations with data measures.
Weak solutions for some reaction-diffusion systems with balance law and critical growth with respect to the gradient