相关论文: Uniqueness and continuous dependence for a viscoel…

In this article, we study the singular case of an homogeneous generalized discrete time system with given initial conditions. We consider the matrix pencil singular and provide necessary and sufficient conditions for existence and…

We present an abstract framework for treating the theory of well-posedness of solutions to abstract parabolic partial differential equations on evolving Hilbert spaces. This theory is applicable to variational formulations of PDEs on…

In this note, we consider a viscous incompressible fluid in a finite domain in both two and three dimensions, and examine the question of determining degrees of freedom (projections, functionals, and nodes). Our particular interest is the…

In this paper, we investigate properties of unique continuation for hyperbolic Schr\"odinger equations with time-dependent complex-valued electric fields and time-independent real magnetic fields. We show that positive masses inside of a…

We obtain explicit estimates on the stability of the unique continuation for a linear system of hyperbolic equations. In particular our result applies to the elasticity system and also the Maxwell system. As an application, we study the…

It is shown that Navier Stokes equation models with time dependent external forces in L2 can have singular solutions.

Time-dependent plasma codes are a natural extension of static nonequilibrium plasma codes. Comparing relevant timescales will determine whether or not time-dependent treatment is necessary. In this article I outline the ingredients for a…

We study stochastic resetting of a probe particle in a viscoelastic environment where only the probe is reset while the medium retains memory of its past dynamics. Using a minimal model with finite correlation time, we analyze the…

A conservative invariant domain preserving Arbitrary Lagrangian Eulerian method for solving nonlinear hyperbolic systems is introduced. The method is explicit in time, works with continuous finite elements and is first-order accurate in…

We study one-dimensional linear hyperbolic systems with $L^{\infty}$-coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of…

We study a coupled system of Navier-Stokes equation and the equation of conservation of mass in a one-dimensional network. The system models the blood circulation in arterial networks. A special feature of the system is that the equations…

In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a…

In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…

Parameter identifiability is often requisite to the effective application of mathematical models in the interpretation of biological data, however theory applicable to the study of partial differential equations remains limited. We present…

We consider the elasticity problem in a %heterogeneous domain with contact on multiple periodic open cracks. The contact is described by the Signorini and Coulomb-friction conditions. Problem is non-linear, the dissipative functional…

This paper consists of two parts. In the first part we prove the unique solvability for the abstract variational-hemivariational inequality with history-dependent operator. The proof is based on the existing result for the static…

In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…

In this paper, we consider an inverse problem for three dimensional viscoelastic fluid flow equations, which arises from the motion of Kelvin-Voigt fluids in bounded domains (a hyperbolic type problem). This inverse problem aims 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…

In this paper we study first order hyperbolic systems with multiple characteristics (weakly hyperbolic) and time-dependent analytic coefficients. The main question is when the Cauchy problem for such systems is well-posed in $C^{\infty}$…