Conservation laws for a coupled variable-coefficient modified Korteweg–de Vries system in a two-layer fluid model

We find the Lie point symmetries of a coupled variable-coefficient modified Korteweg–de Vries system in a two-layer fluid model. Then we establish its quasi self-adjointness and corresponding conservation laws.     

On a two-component Degasperis–Procesi shallow water system

We consider a two-component Degasperis–Procesi system which arises in shallow water theory. We analyze some aspects of blow up mechanism, traveling wave solutions and the persistence properties. Firstly, we discuss the local well-posedness and blow up criterion; a new blow up criterion for this system with the initial odd condition will be established. Finally, the persistence properties of strong solutions will also be investigated.     

A continuous model for production–distribution system design

The production–distribution system design problem (PDSDP) involves decisions concerning the structure of a firm's supply chain. An overwhelming majority of the literature uses mixed integer programming formulations in representing such facility design decisions. In this paper, we present an alternative modeling framework, which is based on the use of continuous functions to represent spatial distributions of cost and customer demand. The proposed continuous model allows the derivation of a number of insights about the impact of problem parameters on facility design decisions. It is proposed that discrete and continuous modeling approaches complement each other.     

Global wellposedness for a one-dimensional Chern–Simons–Dirac system in Lp

The global wellposedness in L^p(?) for the Chern–Simons–Dirac equation in the 1+1 space and time dimension is discussed. We consider two types of quadratic nonlinearity: the null case and the non-null case. We show the time global wellposedness for the Chern–Simon–Dirac equation in the framework of L^p(?), where 1≤p≤∞ for the null case. For the scaling critical case, p = 1, mass concentration phenomena of the solutions may occur in considering the time global solvability. We invoke the Delgado–Candy estimate which plays a crucial role in preventing concentration phenomena of the global solution. Our method is related to the original work of Candy (2011), who showed the time global wellposedness for the single Dirac equation with cubic nonlinearity in the critical space L²(?).     

Vortices in a 2d rotating Bose–Einstein condensate

We investigate the physical model for a two dimensional rotating Bose–Einstein condensate. We minimize a Gross–Pitaevskii functional defined in ${\mathbb{R}}^2$ under the unit mass constraint. We estimate the critical rotational speeds ${\Omega }_d$ for having d vortices in the condensate and we determine the location of the vortices. This relies on an asymptotic expansion of the energy. To cite this article: R. Ignat, V. Millot, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Coexistence in a competitor–competitor–mutualist model

This paper is concerned with a system modeling a competitor–competitor–mutualist three-species Lotka–Volterra model. By Schauder fixed point theory, the existence of positive solutions to a strongly coupled elliptic system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed and a numerical simulation is also presented. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak.     

Coupling of a one-dimensional river routing model and a three-dimensional ocean model to predict overbank flows in a complex river–ocean system

River–ocean coupled models were developed to calculate overbank flows in a complex river–coastal ocean system comprising the Wu River and the adjacent coastal ocean of central Taiwan. The hydrodynamic quantities were exchanged between one-dimensional and three-dimensional domains during runtime to resolve the real-time exchange and interaction between the coastal waters and the river system. The coupled model was calibrated and verified with the observed water levels using data from three typhoon events. The results indicate a reasonable agreement between the model simulations and the observed data. The model was then used to calculate hydrographs of the overbank flow caused by Typhoon Kalmaegi, which occurred in 2008. The simulated overbank flows quantitatively agreed with the reported information. We also demonstrated that most of the overbank flows occurred at the upper reaches of the tributaries of the Wu River system, except for the tributary in the Fazi River.     

Robust equilibrium reinsurance-investment strategy for a mean–variance insurer in a model with jumps

This paper analyzes the equilibrium strategy of a robust optimal reinsurance-investment problem under the mean–variance criterion in a model with jumps for an ambiguity-averse insurer (AAI) who worries about model uncertainty. The AAI’s surplus process is assumed to follow the classical Cramér–Lundberg model, and the AAI is allowed to purchase proportional reinsurance or acquire new business and invest in a financial market to manage her risk. The financial market consists of a risk-free asset and a risky asset whose price process is described by a jump-diffusion model. By applying stochastic control theory, we establish the corresponding extended Hamilton–Jacobi–Bellman (HJB) system of equations. Furthermore, we derive both the robust equilibrium reinsurance-investment strategy and the corresponding equilibrium value function by solving the extended HJB system of equations. In addition, some special cases of our model are provided, which show that our model and results extend some existing ones in the literature. Finally, the economic implications of our findings are illustrated, and utility losses from ignoring model uncertainty, jump risks and prohibiting reinsurance are analyzed using numerical examples.     

Solution of the Bitsadze–Samarskii problem for a parabolic system in a semibounded domain

We consider a nonlocal initial–boundary value Bitsadze–Samarskii problem for a spatially one-dimensional parabolic second-order system in a semibounded domain with nonsmooth lateral boundary. The boundary integral equation method is used to construct a classical solution of this problem under the condition that the vector function on the right-hand side in the nonlocal boundary condition only has a continuous derivative of order 1/2 vanishing at t = 0. The smoothness of the solution is studied.     

Complex behaviour in a production–distribution model

The purpose of this paper is to show how the cascaded structure of a production–distribution chain can produce a wide variety of dynamic behaviours. Despite the apparent simplicity of the chain, the bounded rationality of human decision making interferes with the information feedbacks, nonlinearities and time delays of the system to produce exceedingly complex behaviour. When simulated with realistic parameter values, the model can exhibit stationary periodic, quasiperiodic as well as chaotic and hyperchaotic motions. Lyapunov exponents are used to characterize the different types of behaviour. Repeated simulation reveals how the profile of operating cost is related to the modes of behaviour and to the conditions that generate chaos. Detailed maps of parameter space graphically show the influence of inventory control policies upon dynamics and costs. The analyses illustrate why it is so difficult for decision makers to “navigate” in low-cost policy parameter regions. Suggestions are made for decision heuristics that avoid high-cost, unstable solutions.     

The giant vortex state for a Bose–Einstein condensate in a rotating anharmonic trap: Extreme rotation regimes

We study the fast rotation limit for a Bose–Einstein condensate in a quadratic plus quartic confining potential within the framework of the two-dimensional Gross–Pitaevskii energy functional. As the rotation speed tends to infinity with a proper scaling of the other parameters in the model, a linear limit problem appears for which we are able to derive precise energy estimates. We prove that the energy and density asymptotics of the problem can be obtained by minimizing a simplified one-dimensional energy functional. In the case of a fixed coupling constant we also prove that a giant vortex state appears. It is an annulus with pure irrotational flow encircling a central low-density hole around which there is a macroscopic phase circulation.     

Orbits in a stochastic Goodwin–Lotka–Volterra model

This paper examines the cycling behavior of a deterministic and a stochastic version of the economic interpretation of the Lotka–Volterra model, the Goodwin model. We provide a characterization of orbits in the deterministic highly non-linear model. We then study a stochastic version, with Brownian noise introduced via a heterogeneous productivity factor. Existence conditions for a solution to the system are provided. We prove that the system produces cycles around a unique equilibrium point in finite time for general volatility levels, using stochastic Lyapunov techniques for recurrent domains. Numerical insights are provided.     

Bogdanov–Takens bifurcation in a predator–prey model

In this paper, we investigate a class of predator–prey model with age structure and discuss whether the model can undergo Bogdanov–Takens bifurcation. The analysis is based on the normal form theory and the center manifold theory for semilinear equations with non-dense domain combined with integrated semigroup theory. Qualitative analysis indicates that there exist some parameter values such that this predator–prey model has an unique positive equilibrium which is Bogdanov–Takens singularity. Moreover, it is shown that under suitable small perturbation, the system undergoes the Bogdanov–Takens bifurcation in a small neighborhood of this positive equilibrium.