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This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
We consider an inverse boundary problem for the dynamical Maxwell's equations. We show that the electric permittivity, conductivity, and magnetic permeability can be uniquely determined locally if there is a strictly convex foliation with…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…
This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion equations. Starting from a high-order spatial baseline…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
A system of a first order history-dependent evolutionary variational-hemivariational inequality with unilateral constraints coupled with a nonlinear ordinary differential equation in a Banach space is studied. Based on a fixed point theorem…
We study the nonhomogeneous boundary value problem for Navier--Stokes equations of steady motion of a viscous incompressible fluid in a two--dimensional bounded multiply connected domain $\Omega=\Omega_1\setminus\bar{\Omega}_2,…
We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…
This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and…
We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment…
We establish uniform a-priori estimates for solutions of the semilinear Dirichlet problem \begin{equation} \begin{cases} (-\Delta)^m u=h(x,u)\quad&\mbox{in }\Omega,\\ u=\partial_nu=\cdots=\partial_n^{m-1}u=0\quad&\mbox{on }\partial\Omega,…
Let $u$ be the solution to the following stochastic evolution equation (1) du(t,x)& = &A u(t,x) dt + B \sigma(u(t,x)) dL(t),\quad t>0; u(0,x) = x taking values in an Hilbert space $\HH$, where $L$ is a $\RR$ valued L\'evy process, $A:H\to…
We study the mathematical properties of time-dependent flows of incompressible fluids that respond as an Euler fluid until the modulus of the symmetric part of the velocity gradient exceeds a certain, a-priori given but arbitrarily large,…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to…
We establish general quantitative conditions for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise in variational formulation resulting in the existence of a unique invariant probability measure…
We consider the classic spring-mass model of running which is built upon an inverted elastic pendulum. In a natural way, there arises an interesting boundary value problem for the governing system of two nonlinear ordinary differential…
We prove global-in-time existence and uniqueness of measure solutions of a nonlocal interaction system of two species in one spatial dimension. For initial data including atomic parts we provide a notion of gradient-flow solutions in terms…
In this paper, we study evolutive Hamilton Jacobi equations with Hamiltonians that are discontinuous in time, posed on a simple network consisting of two edges on the real line connected at a single junction. We introduce a notion of…