Existence and Nonexistence of Global Classical Solutions to Porous Medium and Plasma Equations with Singular Sources

Let Ω be a bounded or unbounded domain in R^n. The initial-boundary value problem for the porous medium and plasma equation with singular terms is considered in this paper. Criteria for the appearance of quenching phenomenon and the existence of global classical solution to the above problem are established. Also, the life span of the quenching solution is estimated or evaluated for some domains.     

THE QUENCHING OF SOLUTION OF SEMILINEAR PARABOLIC SYSTEMS

This paper deals with the quenching of the solutions for semilinear parabolic systems Conditions under which quenching occurs in finite time and the condition for the existence of global solution are given.     

Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition

In this paper we consider the finite time quenching behavior of solutions to a semilinear heat equation with a nonlinear Neumann boundary condition. Firstly, we establish conditions on nonlinear source and boundary to guarantee that the solution doesn＇t quench for all time. Secondly, we give sufficient conditions on data such that the solution quenches in finite time, and derive an upper bound of quenching time. Thirdly, undermore restrictive conditions, we obtain a lower bound of quenching time. Finally, we give the exact bounds of quenching time of a special example.     

QUENCHING PROBLEMS OF DEGENERATE FUNCTIONAL REACTION-DIFFUSION EQUATION

This paper is concerned with the quenching problem of a degenerate functional reaction-diffusion equation. The quenching problem and global existence of solution for the reaction-diffusion equation are derived and, some results of the positive steady state solutions for functional elliptic boundary value are also presented.     

ON THE CAUCHY PROBLEM FOR A REACTION-DIFFUSION SYSTEM WITH SINGULAR NONLINEARITY

We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） quenches at the originx = 0 at the same time ＇1＇ （see Theorem 4.3）. We also tind various other conditions tor the solution to quench in a finite time and obtain the corresponding decay rate of the solution near the quenching time.     

THE SINGLE-POINT QUENCHING OF NONLINEAR DEGENERATE FUNCTIONAL REACTION-DIFFUSION EQUATION

This article is concerned with the quenching phenomena of the nonlinear degenerate functional reaction-diffusion equation. Some results are obtained on the single-point quenching and the uniqueness of quenching.     

Critical Quenching Exponents for Heat Equations Coupled with Nonlinear Boundary Flux

We discuss the quenching phenomena for a system of heat equations coupled with nonlinear boundary flux. We determine a critical value for the exponents in the boundary flux, such that only in the super critical case the simultaneous quenching can happen for any solution.     

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation （1） are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.     

ASYMPTOTIC ESTIMATION FOR SOLUTION OF A CLASS OF SEMI-LINEAR ROBIN PROBLEMS

A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution.     

有理插值的扩展方程组与约束方程组

Firstly, using the elementary solution, this paper provides the fundammental structure of the general solution of the (m/n)f system of equations in the rational interpolating problem, and points out the significance of the elementary solution. Secondly, it introduces the systems of extended equations and of constrained equations, analyses their properties, gives the structures of their general solution, obtains the relations of both them and the elementary solution, reveals the importance of their describing the elementary solution. And lastly , it computes an example for the two kinds of svstems.     

Lump Solutions,Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations北大核心CSCD

Based on the bilinear form of the generalized (3+1)-dimensional KdV equation, the lump solution, the interaction solution and the breather solution of the equation were obtained. The obtained lump solutions were proved to be rationally localized in all directions of the space, then the “fusion” and “fission” phenomena were observed during the interaction between the lump soliton wave and the one-stripe soliton. Finally, the breather solution of the equation was obtained. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

SINGULAR PERTURBATION OF THREE-POINT BOUNDARY VALUE PROBLEM FOR THIRD ORDER DIFFERENTIAL EQUATIONS

In this paper, by the theory of differential inequalities, we study the existence and uniqueness of the solution to the three-point boundary value problem for third order differential equations. Furthermore we study the singular perturbation of three-point boundary value problem to third order quasilinear differential equations, construct the higher order asymptotic solution and get the error estimate of asymptotic solution and perturbed solution.     

PSEUDOPOTENTIAL METHOD APPLIED TO KdV EQUATION AND HIGHER DEGREE KdV EQUATION

In this paper,pseudopotential method is applied to KdV equation and higher degree KdV equation. For KdV equation we find the relative connection between pseudopotential and various travelling wave solutions of KdV equation, i. e. the discontinuous solution, the unbounded periodic solution and the soliton-like solution of KdV equation are determined by zero of pseudopotential function. The pseudopotential and solitary wave solution of the higher degree KdV equation and n-dimension higher degree KdV equation are presented.     

任意除环上一矩阵方程组的一般解与中心和反中心对称解

Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.     

关于Reissner厚板模型的解——对“关于简支厚板与薄板的关系”的讨论

In this paper, the method proposed in [2] is extended to the case of thickplate, the problem in the solution of Reissner model of thick plate is reduced to a solution oftwo displacement functions ω and f, and the general form of the solution of this model isderived. For a simply supported polygonal thick plate, f vanishes identically, and hence therelation between the solution of thick plate and that of similar thin plate can be established.According to this relation, the solutions of a class of thick plates may be derived from thecorresponding solutions of thin plates.     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF STRONGLY NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the singularly perturbed theory and the boundary layer corrective method, the asymptotic behavior of solution for a class of strongly nonlinear non-autonomous equations and the infection for asymptotic behavior of the solution with regard to the boundary condition are studied. According to the different regions of the boundary value, the asymptotic expansions of the solution for the original problem are obtained simply and conveniently.     

带无限时滞中立型随机泛函微分方程的解的存在唯一性

In this paper, we will make use of a new method to study the existence and uniqueness for the solution of neutral stochastic functional differential equations with infinite delay (INSFDEs for short) in the phase space BC((?∞,0];Rd). By constructing a new iterative scheme, the existence and uniqueness for the solution of INSFDEs can be directly obtained only under uniform Lipschitz condition, linear grown condition and contractive condition. Meanwhile, the moment estimate of the solution and the estimate for the error between the approximate solution and the accurate solution can be both given. Compared with the previous results, our method is partially different from the Picard iterative method and our results can complement the earlier publications in the existing literatures.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEM

In this paper we prove the existence and uniqueness of the solution for a class of nonlinear fractional differential system, and investigate the dependence of the solution on the orderαi.     

Mild Solution of Stochastic Equations with Levy Jumps： Existence, Uniqueness, Regularity and Stability

The existence and uniqueness of mild solution to stochastic equations with jumps are established, a stochastic Fubini theorem and a type of Burkholder-Davis- Gundy inequality are proved, and the two formulas are used to study the regularity property of the mild solution of a general stochastic evolution equation perturbed by Levy process. Then the authors prove the moment exponential stability, almost sure exponential stability and comparison principles of the mild solution. As applications, the stability and comparison principles of stochastic heat equation with Levy jump are given.     

The Singularly Perturbed Nonlinear Nonlocal Initial Boundary Value Problems for Reaction Diffusion Equations

The singularly perturbed nonlinear nonlocal initial boundary value problem for reaction diffusion equations is discussed. Under suitable conditions, the outer solution of the original problem is obtained. By using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. By using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied, and by educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are considered.