相关论文: A thresholding algorithm to Willmore-type flows vi…

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on $R^d$ are studied. These equations constitute gradient flows for the perturbed information functionals $F[u] = 1/(2\alpha)…

In this article we present a new strategy of addressing the (variable coefficient) thin obstacle problem. Our approach is based on a (variable coefficient) Carleman estimate. This yields semi-continuity of the vanishing order, lower and…

We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…

Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic…

We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…

We establish a deep connection between the Prandtl equations linearised around a quadratic shear flow, confluent hypergeometric functions of the first kind, and the Schr\"odinger operator. Our first result concerns an ODE and a spectral…

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability.…

The All-Pairs Max-Flow problem has gained significant popularity in the last two decades, and many results are known regarding its fine-grained complexity. Despite this, wide gaps remain in our understanding of the time complexity for…

We consider a free boundary problem for the Willmore functional. Given a smooth domain $\Omega$ in ${\mathbb R}^3$, we construct Willmore disks wich are critical in the class of surfaces meeting $\partial \Omega$ orthogonally along their…

We propose a randomized algorithm with query access that given a graph $G$ with arboricity $\alpha$, and average degree $d$, makes $\widetilde{O}\left(\frac{\alpha}{\varepsilon^2d}\right)$ \texttt{Degree} and…

Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…

We present Oseen equations on Lipschitz domains in a port-Hamiltonian context. Such equations arise, for instance, by linearization of the Navier-Stokes equations. In our setup, the external port consists of the boundary traces of velocity…

We investigate the mass-preserving $L^2$-gradient flow associated with a generalized Cahn--Hilliard equation. Our focus is on the sharp interface regime, where the interface width parameter $\varepsilon > 0$ is small. For well-prepared…

In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection…

The link to the online abstract of this manuscript, accepted in Phys. Rev. Fluids, is https://journals.aps.org/prfluids/accepted/32074S4aH8b1c608e19768b42571f9001086a3f44. A subcritical route to turbulence via purely quasi-two-dimensional…

A boundary value problem related to a third- order parabolic equation with a small parameter is analized. This equation models the one-dimensional evolution of many dissipative media as viscoelastic fluids or solids, viscous gases,…

Mixed level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao and Gilbert-Varshamov type bounds for mixed level orthogonal arrays. The computational complexity of the terms involved…

We study the maximum $s,t$-flow oracle problem on planar directed graphs where the goal is to design a data structure answering max $s,t$-flow value (or equivalently, min $s,t$-cut value) queries for arbitrary source-target pairs $(s,t)$.…

Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond to the intended sharp interface evolution. Here we introduce a new two-variable diffuse approximation that…

We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of {F}orchheimer-type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a…