Zobrazeno 1 - 10
of 1 173
pro vyhledávání: '"35B25"'
We study the exchange of stability in scalar reaction-diffusion equations which feature a slow passage through transcritical and pitchfork type singularities in the reaction term, using a novel adaptation of the geometric blow-up method. Our results
Externí odkaz:
http://arxiv.org/abs/2411.13679
Autor:
Mel'nyk, Taras, Rohde, Christian
A reduced-dimensional asymptotic modelling approach is presented for the analysis of two-phase flow in a thin cylinder with aperture of order $\mathcal{O}(\varepsilon),$ where $\varepsilon$ is a small positive parameter. We consider a nonlinear Muska
Externí odkaz:
http://arxiv.org/abs/2411.02923
Autor:
Solci, Margherita
We study the asymptotic behaviour of double-well energies perturbed by a higher-order fractional term, which, in the one-dimensional case, take the form $$ \frac{1}{\varepsilon}\int_I W(u(x))dx+\varepsilon^{2(k+s)-1}\frac{s(1-s)}{2^{1-s}}\int_{I\time
Externí odkaz:
http://arxiv.org/abs/2411.01586
In this study, we provide a detailed analysis of the spike solutions and their stability for theGierer-Meinhardt model on discrete lattices. We explore several phenomena that have no analogues in the continuum limit. For example in the discrete case,
Externí odkaz:
http://arxiv.org/abs/2410.05692
Autor:
Ikeda, Hideo, Kuwamura, Masataka
Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using the analyt
Externí odkaz:
http://arxiv.org/abs/2410.06404
In some models, periodic configurations can be shown to be stable under, both, global $\ell^2$ or local perturbations. This is not the case for aperiodic media. The specific class of aperiodic media we are interested, in arise from taking two 2D peri
Externí odkaz:
http://arxiv.org/abs/2409.06151
In this article, we study a system of reaction-diffusion equations in which the diffusivities are widely separated. We report on the discovery of families of spatially periodic canard solutions that emerge from {\em singular Turing bifurcations}. The
Externí odkaz:
http://arxiv.org/abs/2409.02400
In this article, we establish variational characterization of solutions of a mixed local and nonlocal singular semilinear elliptic problem. As an application of this fact, we deduce decomposition property. Further, using moving plane method, we prove
Externí odkaz:
http://arxiv.org/abs/2408.09924
Autor:
Hintz, Peter
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime $(M,g)$ satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic $\mathcal{C}$, we construct, on any compact subset of $M$, s
Externí odkaz:
http://arxiv.org/abs/2408.06715
Autor:
Hintz, Peter
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime $(M,g)$ satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic $\mathcal{C}$, we constructed in Part I a family of metrics
Externí odkaz:
http://arxiv.org/abs/2408.06712