相关论文: Eigenelements of a General Aggregation-Fragmentati…

We derive a nonlinear integro-differential transport equation describing collective evolution of weights under gradient descent in large-width neural-network-like models. We characterize stationary points of the evolution and analyze…

We consider the linear growth and fragmentation equation with general coefficients. Under suitable conditions, the first eigenvalue represents the asymptotic growth rate of solutions, also called \emph{fitness} or \emph{Malthus coefficient}…

In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a…

Given $k:\mathbb{R}^n\setminus\{0\} \to \mathbb{R}^n$ a kernel of class $C^2$ and homogeneous of degree $1-n$, we prove existence and uniqueness of H\"older regular solutions for some non-linear transport equations with velocity fields…

We are interested in the large time behavior of the solutions to the growth-fragmentation equation. We work in the space of integrable functions weighted with the principal dual eigenfunction of the growth-fragmentation operator. This space…

For $0<\nu_2<\nu_1\leq 1$, we analyze a linear integro-differential equation on the space-time cylinder $\Omega\times(0,T)$ in the unknown $u=u(x,t)$ $$\mathbf{D}_{t}^{\nu_1}(\varrho_{1}u)-\mathbf{D}_{t}^{\nu_2}(\varrho_2…

In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…

This paper establishes a theory of nonlinear spectral decompositions by considering the eigenvalue problem related to an absolutely one-homogeneous functional in an infinite-dimensional Hilbert space. This approach is both motivated by…

Fragmentation--coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution,…

We face the well-posedness of linear transport Cauchy problems $$\begin{cases}\dfrac{\partial u}{\partial t} + b\cdot\nabla u + c\,u = f&(0,T)\times{\mathbb R}^n\\u(0,\cdot)=u_0\in L^\infty&{\mathbb R}^n\end{cases}$$ under borderline…

We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant posterior concentration, and pronounced non-Gaussianity. Our…

We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…

We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…

Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling…

This paper deals with the large-scale behaviour of dynamical optimal transport on $\mathbb{Z}^d$-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes…

We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…

We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex…

We consider a coagulation multiple-fragmentation equation, which describes the concentration $c\_t(x)$ of particles of mass $x \in (0,\infty)$ at the instant $t \geq 0$ in a model where fragmentation and coalescence phenomena occur. We…

Eigenproblems frequently arise in theory and applications of stochastic processes, but only a few have explicit solutions. Those which do, are usually solved by reduction to the generalized Sturm--Liouville theory for differential…

Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…