查看更多>>摘要：This study introduces a pre-orthogonal adaptive Fourier decomposition(POAFD)to obtain approximations and numerical solutions to the fractional Laplacian initial value problem and the extension problem of Caffarelli and Silvestre(generalized Poisson equation).As a first step,the method expands the initial data function into a sparse series of the fun-damental solutions with fast convergence,and,as a second step,makes use of the semigroup or the reproducing kernel property of each of the expanding entries.Experiments show the effectiveness and efficiency of the proposed series solutions.
查看更多>>摘要：In this paper,we consider the semilinear elliptic equation systems-△u+u=αQn(x)|u|α-2|v|βu in RN,-△v+v=βQn(X)|u|α|v|β-2v in RN,where N≥3,α,β＞1,α+β＜2*,2*=2N/N-2 and Qn are bounded given functions whose self-focusing cores {x ∈ RN|Qn(x)＞0} shrink to a set with finitely many points as n → ∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.
查看更多>>摘要：In this paper,we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs.Under some appropriate assumptions on the curvature con-dition CDE'(n,0),the polynomial volume growth of degree m,the initial values,and the exponents in absorption terms,we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time.Our current work extends the results achieved by Lin and Wu(Calc Var Partial Differ Equ,2017,56:Art 102)and Wu(Rev R Acad Cien Serie A Mat,2021,115:Art 133).
查看更多>>摘要：In this paper,we study the flocking behavior of a thermodynamic Cucker-Smale model with local velocity interactions.Using the spectral gap of a connected stochastic matrix,together with an elaborate estimate on perturbations of a linearized system,we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking.Moreover,it is shown that the system achieves a consensus at an exponential rate.
查看更多>>摘要：This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
查看更多>>摘要：Let BH be a fractional Brownian motion with Hurst index 1/2 ≤ H＜1.In this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dXHt=dBHt+σXHtdt+vdt-θ(∫t0(XHt-XHs)ds)dt,where θ＜0,σ,v ∈ R.The process is an analogue of self-attracting diffusion(Cranston,Le Jan.Math Ann,1995,303:87-93).Our main aim is to study the large time behaviors of the process.We show that the solution XH diverges to infinity as t tends to infinity,and obtain the speed at which the process XH diverges to infinity as t tends to infinity.
查看更多>>摘要：Motivated by some recent works on the topic of the Brown-Resnick process,we study the functional limit theorem for normalized pointwise maxima of dependent chi-processes.It is proven that the properly normalized pointwise maxima of those processes are attracted by the Brown-Resnick process.
查看更多>>摘要：In this article,a novel scalarization technique,called the improved objective-constraint approach,is introduced to find efficient solutions of a given multiobjective pro-gramming problem.The presented scalarized problem extends the objective-constraint prob-lem.It is demonstrated that how adding variables to the scalarized problem,can lead to find conditions for(weakly,properly)Pareto optimal solutions.Applying the obtained necessary and sufficient conditions,two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed.These algorithms are easy to implement and can achieve an even approximation of(weakly,properly)Pareto op-timal solutions.These algorithms can be generalized for optimization problems with more than three criterion functions,too.The effectiveness and capability of the algorithms are demonstrated in test problems.
查看更多>>摘要：In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of RN,N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.
查看更多>>摘要：This work presents an advanced and detailed analysis of the mechanisms of hep-atitis B virus(HBV)propagation in an environment characterized by variability and stochas-ticity.Based on some biological features of the virus and the assumptions,the corresponding deterministic model is formulated,which takes into consideration the effect of vaccination.This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations.The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative α-stable jumps.By developing the assumptions and employing the novel theoretical tools,the threshold parameter responsible for ergodicity(persistence)and extinction is provided.The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed.Moreover,we obtain the following new interesting findings:(a)in each class,the average time depends on the value ofα;(b)the second-order noise has an inverse effect on the spread of the virus;(c)the shapes of population densities at stationary level quickly changes at certain values of α.The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.
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