Zobrazeno 1 - 10
of 59
pro vyhledávání: '"de Rijk, Björn"'
Autor:
Alexopoulos, Joannis, de Rijk, Björn
Recently, a nonlinear stability theory has been developed for wave trains in reaction-diffusion systems relying on pure $L^\infty$-estimates. In the absence of localization of perturbations, it exploits diffusive decay caused by smoothing together wi
Externí odkaz:
http://arxiv.org/abs/2409.17859
Autor:
Garénaux, Louis, de Rijk, Björn
For a viscous Klein-Gordon equation with quadratic nonlinearity, we prove that small solutions exist on exponentially long time scale. Our approach is based on the space-time resonance method in a diffusive setting. It allow to identify, through a si
Externí odkaz:
http://arxiv.org/abs/2402.02220
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate pattern selectio
Externí odkaz:
http://arxiv.org/abs/2310.08765
We study the nonlinear dynamics of perturbed, spectrally stable $T$-periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. It is known that for each
Externí odkaz:
http://arxiv.org/abs/2307.01176
Autor:
de Rijk, Björn
We present a nonlinear stability theory for periodic wave trains in reaction-diffusion systems, which relies on pure $L^\infty$-estimates only. Our analysis shows that localization or periodicity requirements on perturbations, as present in the curre
Externí odkaz:
http://arxiv.org/abs/2205.04272
The real Ginzburg-Landau equation arises as a universal amplitude equation for the description of pattern-forming systems exhibiting a Turing bifurcation. It possesses spatially periodic roll solutions which are known to be stable against localized p
Externí odkaz:
http://arxiv.org/abs/2201.12156
Using various techniques from dynamical systems theory, we rigorously study an experimentally validated model by [Barkley et al., Nature, 526:550-553, 2015], which describes the rise of turbulent pipe flow via a PDE system of reduced complexity. The
Externí odkaz:
http://arxiv.org/abs/2108.09990
We consider the nonlinear stability of spectrally stable periodic waves in the Lugiato-Lefever equation (LLE), a damped nonlinear Schr\"odinger equation with forcing that arises in nonlinear optics. So far, nonlinear stability of such solutions has o
Externí odkaz:
http://arxiv.org/abs/2106.01910
We consider a nonlinear chain of coupled oscillators, which is a direct generalization of the classical FPU lattice and exhibits, besides the usual nearest neighbor interaction, also next-to-nearest neighbor interaction. For the case of nearest neigh
Externí odkaz:
http://arxiv.org/abs/2103.14551
It is well-established that Whitham's modulation equations approximate the dynamics of slowly varying periodic wave trains in dispersive systems. We are interested in its validity in dissipative systems with a conservation law. The prototype example
Externí odkaz:
http://arxiv.org/abs/2101.04993