Zobrazeno 1 - 10
of 2 137
pro vyhledávání: '"Markowich, P."'
We consider nonlinear Vlasov-type equations involving powers of the zero-order moment and obtain a local existence and uniqueness result within a framework of analytic functions. The proof employs a Banach fixed point argument, where a contraction ma
Externí odkaz:
http://arxiv.org/abs/2412.04581
Autor:
Markowich, Peter, Portaro, Simone
We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the complex interact
Externí odkaz:
http://arxiv.org/abs/2411.06290
In recent years, the study of biological transportation networks has attracted significant interest, focusing on their self-regulating, demand-driven nature. This paper examines a mathematical model for these networks, featuring nonlinear elliptic eq
Externí odkaz:
http://arxiv.org/abs/2408.15680
We propose a mesoscopic modeling framework for optimal transportation networks with biological applications. The network is described in terms of a joint probability measure on the phase space of tensor-valued conductivity and position in physical sp
Externí odkaz:
http://arxiv.org/abs/2401.07922
We study self-regulating processes modeling biological transportation networks as presented in \cite{portaro2023}. In particular, we focus on the 1D setting for Dirichlet and Neumann boundary conditions. We prove an existence and uniqueness result un
Externí odkaz:
http://arxiv.org/abs/2307.16436
Autor:
Amadori, Debora, Andreianov, Boris, Di Francesco, Marco, Fagioli, Simone, Girard, Théo, Goatin, Paola, Markowich, Peter, Pietschmann, Jan F., Rosini, Massimiliano D., Russo, Giovanni, Stivaletta, Graziano, Wolfram, Marie-Therese
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version of the model, researchers focused on the structure of the Riemann prob
Externí odkaz:
http://arxiv.org/abs/2305.10076
Publikováno v:
Communications on Applied Mathematics and Computation 2023
We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network formation. The numerical method is based on a non-linear finite difference scheme on a uniform Cartesian grid in a 2D domain. The foc
Externí odkaz:
http://arxiv.org/abs/2301.12926
Publikováno v:
Mathematical and Computational Applications 2022
We compare the solutions of two systems of partial differential equations (PDE), seen as two different interpretations of the same model that describes formation of complex biological networks. Both approaches take into account the time evolution of
Externí odkaz:
http://arxiv.org/abs/2209.08292
Publikováno v:
Discrete and Continuous Dynamical Systems, 2023, 43(3&4): 1499-1515
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 broad class of entropy dissipations associated with a purely diffusi
Externí odkaz:
http://arxiv.org/abs/2207.03542
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 permeability tensor under the influence of a diffusion term, repres
Externí odkaz:
http://arxiv.org/abs/2111.03889