We study self-regulating processes modeling biological transportation networks. Firstly, we
write the formal $ L^ 2$-gradient flow for the symmetric tensor valued diffusivity $ D $ of a …

We study an elliptic-parabolic system of partial differential equations describing formation of
biological network structures. The model takes into consideration the evolution of the …

In this paper, we consider a parabolic-elliptic system of partial differential equations in the
three dimensional setting that arises in the study of biological transport networks. We …

The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-
elliptic system arising from biological transport networks. For such problem, we first establish …

In this paper we study the initial boundary value problem for the system\\$-\mbox {{div}}\left
[(I+\mathbf {m}\mathbf {m}^ T)\nabla p\right]= s (x),\\\mathbf {m} _t-\alpha^ 2\Delta\mathbf …

This paper is concerned with a parabolic–elliptic–parabolic system arising from ion transport
networks. It shows that for any properly regular initial data, the corresponding initial …

This paper deals with a parabolic-elliptic-parabolic system arising from ion transport
networks originally proposed by Albi et al.(Anal Appl 14 (1): 185–206, 2016). Our …

In this paper we study the regularity of weak solutions to an elliptic-parabolic system
modeling natural network formation. The system is singular and involves cubic nonlinearity …

In this paper we study partial regularity of weak solutions to the initial boundary value
problem for the system-div\left (I+ m ⊗ m) ∇ p\right= S (x),\∂ _t mD^ 2 Δ mE^ 2 (m ⋅ ∇ p) ∇ …

In this paper we study the modulus of continuity of weak solutions to a singular elliptic
equation in the plane under very weak assumption on the integrability of the elliptic …