Related papers: Existence of weak solutions for two-phase matrix-v…
We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain discontinuous martingales on Riemannian manifolds from the image of symmetric stable processes…
A fluid-particle system of the inhomogeneous Navier-Stokes equations and Vlasov equation in the three dimensional space is considered in this paper. The coupling arises from the drag force in the fluid equations and the acceleration in the…
We first prove stochastic representation formulae for space-time harmonic mappings defined on manifolds with evolving Riemannian metric. We then apply these formulae to derive Liouville type theorems under appropriate curvature conditions.…
Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more…
The Navier-Stokes-Fourier system is a well established model for describing the motion of viscous compressible heat-conducting fluids. We study the existence of time-periodic weak solutions and improve the known result in the following…
We prove existence of global in time weak solutions to a compressible two-fluid Stokes system with a single velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an…
We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated that the phase transition lines (free boundaries) correspond to…
In the present paper, we study a double-phase variable exponent problem which is set up within a variational framework including a singular potential of fractional-Hardy-type. We employ the Mountain-Pass theorem and the strong minimum…
We follow the idea of Wang \cite{W} to show the existence of global weak solutions to the Cauchy problems of Landau-Lifshtiz type equations and related heat flows from a $n$-dimensional Euclidean domain $\Om$ or a $n$-dimensional closed…
The Teichm\"uller harmonic map flow is a gradient flow for the harmonic map energy of maps from a closed surface to a general closed Riemannian target manifold of any dimension, where both the map and the domain metric are allowed to…
The notes are an overview of part of the theory of pathwise weak solutions to two classes of scalar fully nonlinear first- and second-order degenerate parabolic partial differential equations with multiplicative rough time dependence, a…
A double-well energy expressed as a minimum of two quadratic functions, called phase energies, is studied with taking into account the minimization of the corresponding integral functional. Such integral, as being not sequentially weakly…
In this paper, we propose a numerical method for the solution of time-dependent flow problems in mixed form. Such problems can be efficiently approximated on hierarchical grids, obtained from an unstructured coarse triangulation by using a…
Recent investigations have established the physical relevance of spatially-localized instability mechanisms in fluid dynamics and their potential for technological innovations in flow control. In this letter, we show that the mathematical…
This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
The rectangular multiparameter eigenvalue problem (RMEP) involves rectangular coefficient matrices (usually with more rows than columns) and may potentially have no solution in its original form. A minimal perturbation framework is proposed…
In this paper we study a phase transition model for vehicular traffic flows. Two phases are taken into account, according to whether the traffic is light or heavy. We assume that the two phases have a non-empty intersection, the so called…
We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle…