Nonlinear Analysis-Real World Applications最新文献

The paper focuses on the pattern formation of a chemotactic cell aggregation model with a mechanism that density suppresses motility. The model exhibits four types of cell aggregation patterns: single-point peaks, hot spots, cold spots, and stripes, depending on the parameters and mean density. The analysis is performed in two ways. First, traditional instability analysis reveals the existence of two critical densities. This local analysis shows patterns emerge if the initial mean density lies between the two values. Second, a phase separation method using van der Waals’ double well potential reveals that pattern formation is possible in a bigger parameter regime that includes the one identified by the local analysis. This non-local analysis shows that pattern formation occurs beyond the parameter regimes of the classical local instability analysis.

This paper considers the stabilization problem of the von Kármán beam equation with a combined boundary control of nonlinear delays and nonlinear non-delays. The combined boundary controls are applied at the transverse and longitudinal boundaries of the von Kármán beam, respectively. In this paper the nonlinear semigroup method is adopted in the investigation for the establishment of the well-posedness of the resulting closed-loop system. Constructing an appropriate energy-like function, the exponential decay rate of energy of the closed-loop system is demonstrated by a generalized Gronwall-type integral inequality and the integral multiplier technique.

We study the disease-spreading dynamics of the West Nile virus (WNv) epidemic model under shifting climatic conditions. A WNv epidemic model is developed incorporating a shifting net growth term to depict the evolving mosquito habitat. First, we comprehensively characterize the spreading dynamics of mosquitoes for any given climate change speed compared with the intrinsic spreading speed of mosquitoes. Utilizing the results from mosquito dynamics, we determine the spreading dynamics of infected birds and mosquitoes, taking into account relationships among the shifting speed and the spreading speeds of mosquito and WNv. Ultimately, we find that infected mosquitoes and birds propagate, and their population densities converge to a stable positive endemic state. This paper provides crucial insights into the impact of climate change on the spread of vector-borne diseases such as WNv.

We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of irreversible chemical reactions and assume a nonlinear relation between the pressure and the particular densities. These assumptions cause the additional difficulties in the mathematical analysis, due to the possible presence of vacuum.

It is shown that there exists a global weak solution, satisfying the $L^{\infty }$ bounds for all the components. We obtain strong compactness of the sequence of densities in $L^p$ spaces, under the assumption that all components are strictly positive. The applied method captures the properties of models of high generality, which admit an arbitrary number of components. Furthermore, the framework that we develop can handle models that contain both diffusing and non-diffusing elements.

In general, critical manifold loses normal hyperbolicity at folded, transcritical and pitchfork singularities. There is another situation where normal hyperbolicity of critical manifold fails, namely, the alignment of the tangent and normal bundles at the unbounded part of critical manifold. In this case, how to reveal the attracting or repelling natures of unbounded critical manifold is essential to detect the birth of relaxation oscillations. In this article, after the compactification of the unbounded critical curve and then blowing-up the resulting degenerate line, we find that return mechanism exists at the $O(1/\varepsilon )$-region of the critical curve in a slow–fast excitable Brusselator oscillator. By so doing the birth of relaxation oscillation near the unbounded critical curve in this model is demonstrated. In addition, we reveal the continuation process from Hopf small-amplitude cycle to large relaxation oscillation of size $O(1/\varepsilon )$ in the blown-up space. This may be the counterpart of canard explosion in unbounded situation. All the theoretical predictions are verified by numerical simulations.

We study existence results for a fourth order problem describing single-component film models assuming initial data in Wiener spaces.

The following fully nonlinear attraction–repulsion and zero-flux chemotaxis model is studied: ($♢$)$\left(\begin{array}{c}{u}_t=\nabla \cdot \left({(u+1)}^{m_1-1}\nabla u-\chi u{(u+1)}^{m_2-1}\nabla v\right)\\ \left(+\xi u{(u+1)}^{m_3-1}\nabla w\right)+\lambda u-\mu u^r& \text{in}\Omega \times (0,T_{max}),\\ \tau v_t=\Delta v-\varphi (t,v)+f\left(u\right)& \text{in}\Omega \times (0,T_{max}),\\ \tau w_t=\Delta w-\psi (t,w)+g\left(u\right)& \text{in}\Omega \times (0,T_{max}).\end{array}\right)$Herein, $\Omega$ is a bounded and smooth domain of $R^n$, for $n\in N$, $\chi ,\xi ,\lambda ,\mu ,r$ proper positive numbers, $m_1,m_2$