Related papers: The Expected Time to End the Tug-of-War in a Wedge
In this work, new finite difference schemes are presented for dealing with the upper-convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the…
We construct a finite element method (FEM) for the infinity Laplacian. Solutions of this problem may be singular, which has prompted us to conduct an a posteriori analysis of the method deriving residual based estimators to drive an…
We study a nonlinear stochastic partial differential equation whose solution is the conditional log-Laplace functional of a superprocess in a random environment. We establish its existence and uniqueness by smoothing out the nonlinear term…
The main purpose of this paper is to study the existence of least energy sign-changing solutions for Logarithmic weighted $(N,p)$-Laplacian problem in the unit ball $B$ of $\mathbb{R}^{N},$ $N>2$. The non-linearity of the equation is…
In this paper, we discuss existence and finite speed of propagation for the solutions to an initial-boundary value problem for a family of fractional thin-film equations in a bounded domain in $\mathbb{R}^d$. The nonlocal operator we…
Weights are geometrical degrees of freedom that allow to generalise Lagrangian finite elements. They are defined through integrals over specific supports, well understood in terms of differential forms and integration, and lie within the…
We consider the Dirichlet problem in a wedge for parabolic equation whose coefficients are measurable function of t. We obtain coercive estimates in weighted $L_{p,q}$-spaces. The concept of "critical exponent" introduced in the paper plays…
In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the…
We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some $p$-Laplacian boundary value problems on time scales.
Our previous study [1] has demonstrated that the gauge theory is a proper framework for characterizing the local temporal and spatial interactions in inhomogeneous elastic media. However, in that study temporal interactions were interpreted…
We consider systems of stochastic evolutionary equations of the $p$-Laplace type. We establish convergence rates for a finite-element based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural…
We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We…
Space-time-modulated systems have attracted significant interest over the past decade due to their ability to manipulate electromagnetic waves in unprecedented ways. Here, we introduce a new type of space-time-modulated structure, the…
We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…
We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau…
The exact theory of phase separation in a two-dimensional wedge is derived from the properties of the order parameter and boundary condition changing operators in field theory. For a shallow wedge we determine the passage probability for an…
We consider the game-theoretic approach to time-inconsistent stopping of a one-dimensional diffusion where the time-inconsistency is due to the presence of a non-exponential (weighted) discount function. In particular, we study (weak)…
In this paper, we consider a non-local diffusion equation involving the fractional $p(x)$-Laplacian with nonlinearities of variable exponent type. Employing the sub-differential approach we establish the existence of local solutions. By…
The chase is a widely implemented approach to reason with tuple-generating dependencies (tgds), used in data exchange, data integration, and ontology-based query answering. However, it is merely a semi-decision procedure, which may fail to…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…