Local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity

In this paper,we prove the local existence and uniqueness of solutions to the evolutionary model for magnetoviscoelasticity in R^(2),R^(3).This model consists of an incompressible Navier-Stokes,a regularized system for the evolution of the deformation gradient and the Landau-Lifshitz-Gilbert system for the dynamics of the mag-netization.Our approach depends on approximating the system with a sequence of perturbed systems.

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THERMOMECHANICAL CUCKER-SMALE-STOKES EQUATIONS IN THE WHOLE DOMAIN

We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.

The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms

We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.

The Problems and Solutions of Enterprise Financial Management in the Perspective of Digital Economy

From the perspective of the digital economy,enterprise financial management is facing unprecedented challenges and opportunities.Traditional financial management models are no longer suited to current development needs.Fine-tuning financial management is essential to support the modernization of enterprises,guard against operational risks,and promote coordination across the entire value chain for greater economic efficiency.With the help of digital technology,data-driven,highly interconnected,and intelligent decision-making processes are becoming more prominent,profoundly transforming the operational and financial management models of enterprises.This enables financial management to keep pace with modern developments.In light of this,the paper explores the connotations and mechanisms of the digital economy and enterprise financial management,clarifies relevant conceptual characteristics,and identifies problems in financial management under the digital economy.It also offers strategies for optimization and problem-solving,with the aim of providing valuable insights for educators and practitioners.

THE EXISTENCE AND MULTIPLICITY OF k-CONVEX SOLUTIONS FOR A COUPLED k-HESSIAN SYSTEM

In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.

On existence and uniqueness of the solution of elastoplastic contact problems

Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.

GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY

We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations,with the initial data(u0,B0)being located in the critical Besov space■and the initial densityρ0 being close to a positive constant.By using weighted global estimates,maximal regularity estimates in the Lorentz space for the Stokes system,and the Lagrangian approach,we show that the 2-D MHD equations have a unique global solution.

Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

EXISTENCE, BOUNDEDNESS AND UNIQUENESS OF WEAK SOLUTION FOR THE THERMISTOR PROBLEM WITH MIXED BOUNDARV CONDITIONS

The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION

In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO THE DYNAMIC EQUATIONS FOR KOITER SHELLS

In this paper, the dynamic equations for Koiter shells have been studied by Galerkin method, the existence and uniqueness to the solutions are proved.

The Global Attractor and Its Dimension Estimation of Generalized Kolmogorov-Petrovlkii-Piskunov Equation

In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

ON THE EXISTENCE AND UNIQUENESS OF SOLUTION OF IMPLICIT HYBRID METHODS

In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coefficient condition and its judging criterion as well as the righthand condition to ensure the existing solution uniquely.

Existence and Uniqueness of Weak Solutions to the p-biharmonic Parabolic Equation

We consider an initial-boundary value problem for a p-biharmonic parabolic equation. Under some assumptions on the initial value, we construct approximate solutions by the discrete-time method. By means of uniform estimates on solutions of the time-difference equations, we establish the existence of weak solutions, and also discuss the uniqueness.

ON EXISTENCE， UNIQUENESS AND REGULARITY OF STEADY STATE SOLUTIONS TO THE BASIC SEMICONDUCTOR EQUATIONS

Ealstence and regularity of steady state solutions to the basic semiconductor equations with the non-monotone net recombination rate are proved. A sufficient condition for the uniqueness of the steady state solutions is given. The uniqueness result is very general which contains almost all known conclusions.

THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF GENERALIZED VARIATIONAL INEQUALITIES ARISING FROM ELASTICITY WITH FRICTION

The existence and uniqueness of solutions of generalized variational inequalities arising from elasticity with friction, which is equivalent to corresponding elemental problems, is elucidated in detail, and then FEM approximation and discrete methods are proposed.

Improved Conditions for the Existence and Uniqueness of Solutions to the General Equality Constrained Quadratic Programming Problem

This paper presents an approach that directly utilizes the Hessian matrix to investigate the existence and uniqueness of global solutions for the ECQP problem. The novel features of this proposed algorithm are its uniqueness and faster rate of convergence to the solution. The merit of this algorithm is base on cost, accuracy and number of operations.