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.

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.

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.

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 entire solutions of some Fermat type differential-difference equations

On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].

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.

The existence of radial k-admissible solutions for n-dimension system of k-Hessian equations

In this paper,we focus on a general n-dimension system of k-Hessian equations.By introducing some new suitable growth conditions,the existence results of radial k-admissible solutions of the k-Hessian system are obtained.Our approach is largely based on the well-known fixed-point theorem.

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.

Existence and Stability of Solutions for a Class of Fractional Impulsive Differential Equations with Atangana-Baleanu-Caputo Derivative

In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.

GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC COMPRESSIBLE FLUIDS

The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.

Global Existence and Large Time Asymptotic Behavior of Strong Solution to the Cauchy Problem of 2D Density-Dependent Boussinesq Equations with Vacuum

We dedicate to the 2D density-dependent nonhomogeneous incompressible Boussinesq equations with vacuum on . At infinity, if the attenuation of initial density and temperature is not very slow. And it is gained that there is a global strong solution and is unique for the 2D Cauchy problem with the initial density which can allow vacuum conditions and even have compact support. Besides, the large time decay rates of the gradients of velocity, temperature and pressure can also be obtained which are also the same as those of the homogeneous case.

On Local Existence and Blow-Up of Solutions for Nonlinear Wave Equations of Higher-Order Kirchhoff Type with Strong Dissipation

In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.

Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect

In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. We also prove some nonexistence results.

Global existence of weak solutions to a prey-predator model with strong cross-diffusion

Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.

LOCAL EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS TO THE TWO DIMENSIONAL NONHOMOGENEOUS INCOMPRESSIBLE PRIMITIVE EQUATIONS

In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum is allowed.

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THE 3D COMPRESSIBLE ISOTHERMAL NAVIER-STOKES EQUATIONS

This paper concerns the global existence of strong solutions to the 3 D compressible isothermal Navier-Stokes equations with a vacuum at infinity.Based on the special structure of the Zlotnik inequality,the time uniform upper bounds for density are established through some time-dependant a priori estimates under the assumption that the total mass is suitably small.

Global Existence and Large Time Asymptotic Behavior of Strong Solution to the Cauchy Problem of 2D Density-Dependent Boussinesq Equations of Korteweg Type

In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the initial density and the initial temperature decay not extremely slow. Particularly, it is allowed to be arbitrarily large for the initial data and vacuum states for the initial density, even including the compact support. Moreover, when the density depends on the Korteweg term with the viscosity coefficient and capillary coefficient, we obtain a consistent priority estimate by the energy method, and extend the local strong solutions to the global strong solutions. Finally, when the pressure and external force are not affected, we deform the fluid models of Korteweg type, we can obtain the large time decay rates of the gradients of velocity, temperature and pressure.

GLOBAL EXISTENCE OF SOLUTIONS FOR A STRONGLY COUPLED REACTION-DIFFUSION SYSTEM

This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.

Existence of Positive Solutions for Nonlinear Conjugate Boundary Value Problems

The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.