The foundations of this outstanding book series were laid in 1944. Until the end of the
1970s, a total of 77 volumes appeared, including works of such distinguished …

The concept of entropy is a powerful tool not only in physics and chemistry but also in
mathematics. Entropies allow for the development of new techniques to analyze partial …

This monograph is dedicated to the presentation of The Gradient Discretisation Method
(GDM) and to some of its applications. It is intended for masters students, researchers and …

We prove existence of global weak solutions to the chemotaxis system ut= Δ u−∇⋅(u∇ v)+
κ u− μ u 2 vt= Δ v− v+ u under homogeneous Neumann boundary conditions in a smooth …

The global-in-time existence of bounded weak solutions to a large class of physically
relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is …

In order to become worldly things, that is, deeds and facts and events and patterns of
thoughts or ideas,[action, speech, and thought] must first be seen, heard, and remembered …

The Aubin--Lions lemma and its variants play crucial roles for the existence of weak
solutions of nonlinear evolutionary PDEs. In this paper, we aim to develop some …

This article is dedicated to the no-flux attraction-repulsion chemotaxis model {ut= Δ u−
χ∇⋅(uv∇ v)+ ξ∇⋅(uw∇ w)+ h (u), x∈ Ω, t> 0, vt= Δ v− v+ u, x∈ Ω, t> 0, wt= Δ w− w+ u, x∈ …

The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an
arbitrary number of competing population species is proved. The equations can be derived …

A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number
of population species is analyzed in a bounded domain with no-flux boundary conditions …