Generalized Wasserstein distance and its application to transport equations with source

B Piccoli, F Rossi - Archive for Rational Mechanics and Analysis, 2014 - Springer
In this article, we generalize the Wasserstein distance to measures with different masses.
We study the properties of this distance. In particular, we show that it metrizes weak …

A new optimal transport distance on the space of finite Radon measures

S Kondratyev, L Monsaingeon, D Vorotnikov - 2016 - projecteuclid.org
We introduce a new optimal transport distance between nonnegative finite Radon measures
with possibly different masses. The construction is based on non-conservative continuity …

[LIBRO][B] Spaces of measures and their applications to structured population models

C Düll, P Gwiazda, A Marciniak-Czochra… - 2021 - books.google.com
Structured population models are transport-type equations often applied to describe
evolution of heterogeneous populations of biological cells, animals or humans, including …

Splitting schemes and segregation in reaction cross-diffusion systems

JA Carrillo, S Fagioli, F Santambrogio… - SIAM Journal on …, 2018 - SIAM
One of the most fascinating phenomenon observed in reaction diffusion systems is the
emergence of segregated solutions, ie, population densities with disjoint supports. We …

Structured populations, cell growth and measure valued balance laws

JA Carrillo, RM Colombo, P Gwiazda… - Journal of Differential …, 2012 - Elsevier
A well-posedness theory of measure valued solutions to balance laws is presented.
Nonlinear semigroups are constructed by means of the operator splitting algorithm. This …

Measure solutions for some models in population dynamics

JA Cañizo, JA Carrillo, S Cuadrado - Acta applicandae mathematicae, 2013 - Springer
We give a direct proof of well-posedness of solutions to general selection-mutation and
structured population models with measures as initial data. This is motivated by the fact that …

Structured population models on Polish spaces: A unified approach including graphs, Riemannian manifolds and measure spaces to describe dynamics of …

C Düll, P Gwiazda, A Marciniak-Czochra… - … Models and Methods …, 2024 - World Scientific
This paper presents a mathematical framework for modeling the dynamics of heterogeneous
populations. Models describing local and non-local growth and transport processes appear …

Finite dimensional state representation of physiologically structured populations

O Diekmann, M Gyllenberg, JAJ Metz - Journal of mathematical biology, 2020 - Springer
In a physiologically structured population model (PSPM) individuals are characterised by
continuous variables, like age and size, collectively called their i-state. The world in which …

Mass concentration in a nonlocal model of clonal selection

JE Busse, P Gwiazda, A Marciniak-Czochra - Journal of mathematical …, 2016 - Springer
Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis
requires investigation of the impact of self-renewal on cancer expansion. To better …

On the convergence of the escalator boxcar train

Å Brännström, L Carlsson, D Simpson - SIAM Journal on Numerical …, 2013 - SIAM
The Escalator Boxcar Train (EBT) is a numerical method that is widely used in theoretical
biology to investigate the dynamics of physiologically structured population models, ie …