Related papers: A Note on Singularity Formation for a Nonlocal Tra…
This article considers nonlocal heat flows into a singular target space. The problem is the parabolic analogue of a stationary problem that arises as the limit of a singularly perturbed elliptic system. It also provides a gradient flow…
In the present work we shall consider the existence and multiplicity of solutions for nonlocal elliptic singular problems where the nonlinearity is driven by two convolutions terms. More specifically, we shall consider the following…
We present a lattice-based numerical method to describe the non equilibrium behavior of a simple fluid under non-uniform spatial conditions. The evolution equation for the one-particle phase-space distribution function is derived starting…
We consider an integro-differential equation model for traffic flow which is an extension of the Burgers equation model. To discuss the model, we first examine general settings for integrable integro-differential equations and find that…
An individual-based model of an infinite system of point particles in $\mathbb{R}^d$ is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for…
We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant…
In this paper, we investigate the existence of a finite number of vortex patches for the generalized surface quasi-geostrophic (gSQG) equations with $\alpha \in [1,2)$, focusing on configurations that may rotate uniformly, translate, or…
We consider stochastic equations for the class of formal mappings. Existence and uniqueness of solution, as well as evolution property are proved.
A class of nonlinear Fokker-Planck equations with superlinear drift is investigated in the $L^1$-supercritical regime, which exhibits a finite critical mass. The equations have a formal Wasserstein-like gradient-flow structure with a convex…
The characterization of the solution set for a class of algebraic Riccati inequalities is studied. This class arises in the passivity analysis of linear time invariant control systems. Eigenvalue perturbation theory for the Hamiltonian…
I argue that, within the Closed-Time-Path formalism, pinch singularities do not appear in truly out of equilibrium situations.
Classical as well as quantum features of the late-time evolution of cosmological models with fluids obeying a Shan-Chen-like equation of state are studied. The latter is of the type $p=w_{\rm eff}(\rho)\,\rho$, and has been used in previous…
We study the behaviour near a boundary point a of any positive solution of a nonlinear elliptic equations with forcing term which vanishes on the boundary except at a. Our results are based upon a priori estimates for solutions and…
We study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable, but also on the solution itself. We prove existence, uniqueness and continuous dependence results for…
In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model…
We study surfaces evolving by mean curvature flow (MCF). For an open set of initial data that are $C^3$-close to round, but without assuming rotational symmetry or positive mean curvature, we show that MCF solutions become singular in…
Blow-up solutions to a heat equation with spatial periodicity and a quadratic nonlinearity are studied through asymptotic analyses and a variety of numerical methods. The focus is on the dynamics of the singularities in the complexified…
The search of finite-time singularity solutions of Euler equations is considered for the case of an incompressible and inviscid fluid. Under the assumption that a finite-time blow-up solution may be spatially anisotropic as time goes by…
In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…
This paper describes the variational formulation of template matching problems of computational anatomy (CA); introduces the EPDiff evolution equation in the context of an analogy between CA and fluid dynamics; discusses the singular…