奇异半线性热方程初值问题解的存在性与Blow-up问题

本文讨论如下奇异半线性热方程的初值问题其中γ＞1，σ＞O，f（x）连续有界非负但不恒为零．我们讨论了问题（1），（2）非负局部经典解的存在性和非负整体解的不存在问题，得到当0＜σ＜1且时，（1），（2）没有非负整体解．当σ＝1且时，（1），（2）没有非负整体解，当σ＞1时（1），（2）没有非负整体解．     

关于一类具阻尼项的非线性波方程的Cauchy问题

The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the above-mentioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method.     

On the Nonexistence of Global Weak Solutions to the Navier–Stokes–Poisson Equations in ℝ N

In this paper we prove nonexistence of stationary weak solutions to the Euler–Poisson equations and the Navier–Stokes–Poisson equations in ? ^N , N ≥ 2, under suitable assumptions of integrability for the density, velocity and the potential of the force field. For the time dependent Euler–Poisson equations we prove nonexistence result assuming additionally temporal asymptotic behavior near infinity of the second moment of density. For a class of time dependent Navier–Stokes–Poisson equations in ? ^N this asymptotic behavior of the density can be proved if we assume the standard energy inequality, and therefore the nonexistence of global weak solution follows from more plausible assumption in this case.     

Nonexistence of Solutions of a Semilinear Biharmonic Equation with Singular Potential

The nonexistence of a global solution of the semilinear elliptic equation Δ²u ? (C/|x|⁴)u ? |x|^σ|u|^q = 0 in the exterior of a ball is studied. A sufficient condition for the nonexistence of a global solution is established. The proof is based on the test function method.     

On the existence and nonexistence of solutions of some quasilinear hyperbolic equations

We consider a special class of quasilinear hyperbolic equations of arbitrary order suggested by V.A. Galaktionov. For these equations, we prove the existence of solutions periodic in t > 0 and consider an initial-boundary value problem for which we derive sufficient conditions for the nonexistence of a global solution in the natural energy space of solutions.     

Global well-posedness for strongly damped viscoelastic wave equation

We study the initial boundary value problem for the nonlinear viscoelastic wave equation with strong damping term and dispersive term. By introducing a family of potential wells we not only obtain the invariant sets, but also prove the existence and nonexistence of global weak solution under some conditions with low initial energy. Furthermore, we establish a blow-up result for certain solutions with arbitrary positive initial energy (high energy case)     

Global nonexistence for logarithmic wave equations with nonlinear damping and distributed delay terms

This paper is concerned with global nonexistence of solutions for a logarithmic wave equation with nonlinear damping and distributed delay terms. Due to the simultaneous presence of nonlinear damping and logarithmic source terms, we have difficulty in use of the concavity method. Applying the energy estimates, we show the global nonexistence of solutions with not only non-positive initial energy but also positive initial energy.     

带有阻尼项和源项的波动方程的全局解和爆破解

讨论非线性波动方程(1.1)全局解的存在性和不存在性.当初值满足某些条件时,给出了新的判定全局解是否存在的条件.     

Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions

This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions.For the heat diffusion case,the necessary and sufficient conditions on the global existence of all positive solutions are obtained.For the general fast diffusion case,we get some conditions on the global existence and nonexistence of positive solutions.The results of this paper fill the some gaps which were left in this field.     

The Cauchy Problem for the Generalized IMBq Equation in W(R)

In this paper, the existence and the uniqueness of the global strong solution and the global classical solution for the Cauchy problem of the multidimensional generalized IMBq equation are proved. The nonexistence of the global solution for the Cauchy problem of the generalized IMBq equation is discussed.     

非线性Sobolev-Galpern方程解的blow up

本文研究非线性Ｓｏｂｏｌｅｖ－Ｃａｌｐｅｒｎ方程的初边值问题整体解的不存性即解的爆破问题,用能量估计方法并借助于Ｊｅｎｓｅｎ不等式证明了非线性Ｓｏｂｏｌｉｖ－Ｇａｌｐｅｒｎ方程各种初边值问题在某些假设下不存在整体解。     

Global Cauchy problem for wave equations with a nonlinear damping term

We study the global Cauchy problem for wave equations with a nonlinear damping term. The existence, uniqueness and nonuniqueness, and nonexistence of a global classical solution are considered.     

拟线性抛物方程整体解的存在性和不存在性

The paper studies the existence,the exponential decay and the nonexistence of global solution for a class of quasilinear parabolic equations.     

Positive radially symmetric solution of the Dirichlet problem for a nonlinear elliptic system with <Emphasis Type="Italic">p</Emphasis>-Laplacian

Sufficient conditions for the existence and uniqueness of a positive radially symmetric solution of the Dirichlet problem for a nonlinear elliptic second-order system with p-Laplacian are obtained. In addition, it also proved that these conditions guarantee the nonexistence of a global positive radially symmetric solution.     

One multidimensional version of the Darboux first problem for one class of semilinear second order hyperbolic systems

One multidimensional version of the Darboux first problem for one class of semilinear second order hyperbolic systems is investigated. The questions on local and global solvability and nonexistence of a global solution of this problem are considered.     

Nonexistence of global solutions of the Cauchy problem for systems of klein–Gordon equations with positive initial energy

We study the Cauchy problem for systems of weakly coupled Klein–Gordon equations with dissipations. We prove a theorem on the nonexistence of global solutions with positive initial energy.     

一类非线性卷积拟抛物型积分微分方程整体解的存在性问题

本文研究一类非线性卷积拟抛物型积分微分方程的初边值问题,是运用Galerkin方法结合能量型先验估计证明了其整体强解的存在性、唯一性和正则性，并在一定条件下讨论了整体解的不存在性．     

Global nonexistence of positive initial-energy solutions of a system of nonlinear viscoelastic wave equations with damping and source terms

This work is concerned with a system of viscoelastic wave equations with nonlinear damping and source terms acting in both equations. We prove a global nonexistence theorem for certain solutions with positive initial energy.     

具材料阻尼的非线性双曲型方程整体解的不存在性

考虑了一类具材料阻尼的非线性双曲型方程初边值问题整体解的不存在性．分别采用能量方法、Jensen不等式和凹性方法证明了该问题整体解的不存在性定理．作为主要结果的应用,给出了3个例子．     

A multiplicity result for generalized Laplacian systems with multiparameters

In this paper, we consider the existence, nonexistence and multiplicity of a positive solution for a Gelfand type generalized Laplacian system with a singular indefinite weight and a vector parameter. By using the upper and lower solution method and fixed point index theory, we obtain a global multiplicity result with respect to the parameter.