6 papers
A duality approach to the dense graph limit for biological transportation networks
Nuno J. Alves, Jan Haskovec
We develop a duality-based formulation of the dense graph limit for a variational model of biological transportation networks, where edge conductivities balance pumping power again…
An -theory for -Schrödinger equations with confinement in measure
Nuno J. Alves, José Miguel Urbano
We consider stationary -Schrödinger equations on the whole space with integrable data and potentials that are confining in measure. We introduce asymptotic energy solutions in a…
From nonisothermal BGK to Euler Maxwellians via relative entropy
Nuno J. Alves
We study the hydrodynamic limit of the nonisothermal BGK model toward Euler Maxwellians. For a prescribed sufficiently smooth Euler solution, we use relative entropy to compare a B…
High-friction limit for bipolar Euler-Riesz systems
Nuno J. Alves, Jan Haskovec
We consider a bipolar Euler-Riesz system and rigorously justify the high-friction limit of weak solutions towards a bipolar aggregation-diffusion system with Riesz interactions. Th…
Rigorous dense graph limit of a model for biological transportation networks
Nuno J. Alves, Jan Haskovec
We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with…
Local analytic well-posedness for one-dimensional Vlasov$\unicode{x2013}$Dirac$\unicode{x2013}$Benney-type equations
Nuno J. Alves, Peter Markowich, Athanasios E. Tzavaras
We study a one-dimensional nonlinear Vlasov equation with a local self-consistent force field generated by the density, where the force is given by the spatial derivative of a real…