相关论文: Overcoming Obstacles to Integrability in Perturbed…

An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…

We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…

We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly-oscillatory. Thanks to an averaging…

We consider a periodic evolution inclusion defined on an evolution triple of spaces. The inclusion involves also a subdifferential term. We prove existence theorems for both the convex and the nonconvex problem, and we also produce extremal…

Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…

A simple trick is illustrated, whereby nonlinear evolution equations can be modified so that they feature a lot - or, in some cases, only -- periodic solutions. Several examples (ODEs and PDEs) are exhibited.

Motivated by problems arising in geophysical fluid dynamics, we investigate resonant and near resonant wave interactions in nonlinear wave equations with quadratic nonlinearity, We place a special focus on interactions between slow wave…

The resolution of a very large class of linear and non-linear, stationary and evolutive partial differential problems in the half-space (or similar) under the slip boundary condition is reduced here to that of the corresponding results for…

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…

For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…

Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…

We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized…

Given the complexity of modern software systems, it is of great importance that such systems be able to autonomously modify themselves, i.e., self-adapt, with minimal human supervision. It is critical that this adaptation both results in…

We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity…

This paper considers hyperbolic wave equations with non-local in time conditions involving integrals with respect to time. It is shown that regularity of the solution can be achieved for complexified problem with integral conditions…

A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…

We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…

The aim of this paper is twofold: to prove, for L^1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability…

In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x(\Lambda^s u + u\Lambda^r u^2) = 0, \end{equation*} where…