Local Solution of Three-Dimensional Axisymmetric Supersonic Flow in a Nozzle

In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.

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 Regularity of Local Solutions for a Generalized Camassa-Holm Type Equation

The regularity of the Cauchy problem for a generalized Camassa-Holm type equation is investigated. The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on the initial value of the equation. The local existence of its solution in Sobolev space Hs （R） with 1 〈 s ≤ 3/2 is derived.

Local existence and uniqueness of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow term

In this paper,we prove that there exists a unique local solution for the Cauchy problem of a system of the incompressible Navier-Stokes-Landau-Lifshitz equations with the Dzyaloshinskii-Moriya interaction and V-flow term inR^(2) and R^(3).Our methods rely upon approximating the system with a perturbed parabolic system and parallel transport.

ON THE EXISTENCE OF LOCAL CLASSICAL SOLUTION FOR A CLASS OF ONE-DIMENSIONAL COMPRESSIBLE NON-NEWTONIAN FLUIDS

In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.

LOCALIZED NODAL SOLUTIONS FOR SCHRODINGER-POISSON SYSTEMS

In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x|→∞.We establish,for smallε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal term φu(x)=1/4π∫R^(3)u^(2)(y)/|x−y|dy.Our results improve and extend related ones in the literature.

LOCAL ANALYTIC SOLUTIONS OF A MORE GENERALIZED DHOMBRES EQUATION

We study the local analytic solutions f of the functional equation f（ψ（zf（z））） = φ（f（z）） for z in some neighborhood of the origin. Whether the solution f vanishes at z = 0 or not plays a critical role for local analytic solutions of this equation. In this paper, we obtain results of analytic solutions not only in the case f（0） = 0 but also for f（0） ≠ 0. When assuming f（0） = 0, for technical reasons, we just get the result for f′（0）≠ 0. Then when assuming f（0） = ω0 ≠ 0, ψ（0） = s # 0, ψ（z） is analytic at z = 0 and ψ（z） is analytic at z = ω0, we give the existence of local analytic solutions f in the case of 0 〈 ｜sω0｜ 〈 1 and the case of ｜sω0｜ = 1 with the Brjuno condition.

Local Analytic Solutions of Complete Equations for Mixed Fluid

With the straification theory we have proved the transversal layer s 0 3,k (D) of complete equations for mixed fluid is not an empty set: s 0 3,k (D) ≠ for all k(k≥1) . Based on this conclusion and the “secondary equation” of s 0 3,k (D), this paper fully presents the expressions of coefficients in all local analytic solutions of the equations. Therefore we provide the calculation formulas by which we can get the numerical solutions to any desired accuracy.

Groups Analysis and Localized Solutions of the(2+1)-Dimensional Ito Equation

By means of the modified Clarkson and Kruskal （CK） direct method and the variable separation approach, we investigate the （24-1）-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac-Moody-Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the （2-t-1）-dimensional Ito equation better.

The Localized Method of Fundamental Solution for Two Dimensional Signorini Problems

In this work,the localized method of fundamental solution(LMFS)is extended to Signorini problem.Unlike the traditional fundamental solution(MFS),the LMFS approximates the field quantity at each node by using the field quantities at the adjacent nodes.The idea of the LMFS is similar to the localized domain type method.The fictitious boundary nodes are proposed to impose the boundary condition and governing equations at each node to formulate a sparse matrix.The inequality boundary condition of Signorini problem is solved indirectly by introducing nonlinear complementarity problem function(NCP-function).Numerical examples are carried out to validate the reliability and effectiveness of the LMFS in solving Signorini problems.

GLOBAL SOLUTIONS TO A HYPERBOLIC-PARABOLIC COUPLED SYSTEM WITH LARGE INITIAL DATA

This paper is concerned with the existence of global solutions to the Cauchy problem of a hyperbolic-parabolic coupled system with large initial data. To this end, we first construct its local solutions by the standard iteration technique, then we deduce the basic energy estimate by constructing a convex entropy-entropy flux pair to this system. Moreover, the L∞-estimates and H^2-estimates of solutions are obtained through some delicate estimates. In our results, we do not ask the far fields of the initial data to be equal and the initial data can be arbitrarily large which generalize the result obtained in [7].

GLOBAL EXISTENCE OF THE SOLUTION FOR THE LANDAU-LIFSHITZ EQUATION OF THE FERROMAGNETIC SPIN CHAIN

In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution.

Blow-up of solution for a generalized Boussinesq equation

This paper studies the initial boundary value problem for a generalized Boussinese equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method. Moreover, it gives the sufficient conditions of blow-up of the solution in finite time by using the concavity method.

Blow-up of Solution for a Nonlinear Hyperbolic Equation

In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENT OF NONLINEARITY

The authors of this article study the existence and uniqueness of weak so- lutions of the initial-boundary value problem for ut = div（（｜u｜^δ ＋ d0）｜↓△｜^p（x,t）-2↓△u） ＋ f（x, t） （0 〈 δ 〈 2）. They apply the method of parabolic regularization and Galerkin＇s method to prove the existence of solutions to the mentioned problem and then prove the uniqueness of the weak solution by arguing by contradiction. The authors prove that the solution approaches 0 in L^2 （Ω） norm as t →∞.

Superposition formulas of multi-solution to a reduced(3+1)-dimensional nonlinear evolution equation

We gave the localized solutions,the interaction solutions and the mixed solutions to a reduced(3+1)-dimensional nonlinear evolution equation.These solutions were characterized by superposition formulas of positive quadratic functions,the exponential and hyperbolic functions.According to the known lump solution in the outset,we obtained the superposition formulas of positive quadratic functions by plausible reasoning.Next,we constructed the interaction solutions between the localized solutions and the exponential function solutions with the similar theory.These two kinds of solutions contained superposition formulas of positive quadratic functions,which were turned into general ternary quadratic functions,the coefficients of which were all rational operation of vector inner product.Then we obtained linear superposition formulas of exponential and hyperbolic function solutions.Finally,for aforementioned various solutions,their dynamic properties were showed by choosing specific values for parameters.From concrete plots,we observed wave characteristics of three kinds of solutions.Especially,we could observe distinct generation and separation situations when the localized wave and the stripe wave interacted at different time points.

On Finding Global Smooth Solutions to the Landau-Lifshitz Equation

We prove that n-dimensional radial symmetric Landau-Lifshitz equation possesses at least two classes of global smooth solutions with suitable initial-boundary conditions.

On the Rayleigh-Plateau instability

In this paper,we study the surface instability of a cylindrical pore in the absence of stress.This instability is called the Rayleigh-Plateau instabilty.We consider the model developed by Spencer et al.[18],Kirill et al.[10]and Boutat et al.[2]in the case without stress.We obtain a nonlinear parabolic PDE of order four.We show the local existence and uniqueness of the solution of this problem by using Faedo-Galerkin method.The main results are the global existence of the solution and the convergence to the mean value of the initial data for long time.Numerical tests are also presented in this study.

New simple exact penalty function for constrained minimization

By adding one variable to the equality- or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.

Community-Based Diagnosis for the Improvement of Maternal and Child Protection in the ASACOSEKASI Health Area in the Urban Area of Bamako (Mali)

The community diagnosis is an essential approach to the resolution of health problems with the involvement of the communities concerned who become object and subject. Improvingmaternal and child health is a health priority for many developing countries, including Mali. The objective was to study the role of community-based diagnosis in improving maternal and child protection in a vulnerable urban community in a developing country. Methodology: This was a research-action integrating a community diagnosis conducted in March 2023. The involvement of several stakeholders, including social actors including ASACO, membership card holders, district chiefs, neighborhood delegates, local authorities, and health professionals, made it possible to provide curative, preventive and promotional care. The ASACOSEKA Health Area was used as a setting for the study. The methodology was the indicator approach, contact, document review, interview of CSCOM patients, observation of the structure, prioritization of problems, development of an action plan and restitution of the report. Results: The monograph consisted of describing the characteristics of the study setting. Indeed, the ASACOSEKASI area is located on the left bank of the Niger River, with a population of 34,497 inhabitants. The CSCOM presented to describe a medical unit, a maternity unit, a laboratory unit, an ultrasound room and a medication storage room. The main pathologies found were confirmed simple malaria (45.08%), high AKI: 20.43%, confirmed severe malaria: 19.85%, suspected diarrhoea: 3.43%, trauma related to road accidents: 3.36%, pregnancy-related disorders (1%). BCG, Penta3, VAR, and yellow fever vaccination rates were above 100%. It reflects the fact that the doses administered were higher than the target population. This was related to out-of-area vaccination and lost doses. CPN1, CPN4, tetanus vaccination (VAT2) and family planning (FP) consultations all have a proportion above 100%. Maternal care is increased by out-of-area patients, particularly from Guinea. NPC3 and CPON have a proportion of less than 100%. The target population did not follow policies, standards and procedures. Postpartum, women rarely came to the CPON. Local actions to combat malaria included cleaning up plots and neighbourhoods, weeding families and streets, cleaning gutters, spraying the roosts of the female Anopheles Beetle, sleeping in LLINs, organising chemoprophylaxis days, promoting the use of MS, and using curtains against vectors. Conclusion: The community was involved at all stages of this diagnosis, from design to implementation, as well as to the restitution of local solutions. Indeed, the community diagnosis has led to a resolution plan related to reproductive health.