高阶半线性抛物型方程组的生命跨度

其中m,P,q>1．利用试验函数方法,首先推导一些积分不等式,然后对方程组爆破解的生命跨度 [0,T)给出估计．     

一类非线性Schrodinger方程的整体解和自相似解

对于α的某一取值范围,应用广义Strichartz不等式和压缩映射原理研究了初值在弱Lp空间中足够小的条件下,非线性Schr(o)dinger方程Cauchy问题整体解和自相似解的存在性.     

一类强耦合抛物型方程组初边值问题解的整体存在性

In this paper, we consider a strongly-coupled parabolic system with initial boundary values. Under the appropriate conditions, using Gagliard-Nirenberg inequality, Poincare inequality, Gronwall inequality and imbedding theorem, we obtain the global existence of solutions.     

广义Davey-Stewartson方程组的整体解及自相似解

本文研究Dalvey-Stewartson方程组的整体解与自相似解的存在性.首先,运用Ba- nach不动点定理得到一个关于解整体存在性的一般性定理,然后把一类特殊的初始值用到该存在性结果上去从而得到自相似解存在的结论.     

一类退化非线性抛物型方程整体解的衰减估计

J.L.L ions用紧致性方法证明了一类退化非线性抛物型方程初边值问题整体解的存在唯一性,但解的衰减性很少有人考虑.应用M.N akao建立的差分不等式研究了整体解的衰减估计.     

Integral Inequalities and Global Solutions of Semilinear Evolution Equations

A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.     

Global Solutions to Some Quasilinear Parabolic Systems in Population Dynamics

In this present paper, using the duality technique and the Hölder's inequality, we study the global existence of the solutions to some quasilinear parabolic systems with the cross-diffusion effects in population dynamics.     

三维空间中半线性波动方程组的整体解和自相似解

本文证明了一类半线性波动方程组Cauchy问题整体解的存在唯一性．特别地,证明了自相似解的存在唯一性．同时还得到了渐近自相似解．     

Asymptotically self‐similar global solutions for a higher‐order semilinear parabolic equation

In this paper, we study the higher‐order semilinear parabolic equation where m, p>1 and $a\,\in\,\mathbb{R}$. For p>1+2m/N, we prove that the global existence of mild solutions for small initial data with respect to some norm. Some of those solutions are proved to be asymptotic self‐similar. Copyright © 2009 John Wiley & Sons, Ltd.     

一类非线性Schr(o)dinger方程的整体自相似解

本文应用调和分析的方法研究了一类非线性Sehrodinger方程Cauchy问题整体自相似解的存在唯—性．     

高阶半线性抛物型方程组的生命跨度

本文研究高阶半线性抛物型方程组{ut+(-△)mu=|u|p, (t,x)∈R1+×RN, ut+(-△)mν=|u|q, (t,x)∈R1+×RN,u(0,x)=u0(x),v(0,x)=uo(x),x∈RN,其中m,p,q＞1.利用试验函数方法,首先推导一些积分不等式,然后对方程组爆破解的生命跨度[0,T)给出估计.     

一类双退化非线性抛物型方程

In this paper we study the decay estimate of global solutions to the initialboundary value problem for double degenerate nonlinear parabolic equation by using a difference inequality.     

Lin- Reissner-Tsien方程的自相似解

Lin-Reissner-Tsien方程描述了在跨音速近似下的不稳定跨音速流动.通过相似变换,将Lin-Reissner-Tsien方程简化为一个常微分方程.然后解析求解所得到的方程,并在某些情况下得到的正好是精确解.上述情况下无法得到精确解时,给出了数值模拟.还得到了行波解.     

Source Type Solutions of a Fourth Order Degenerate Parabolic Equation

In this paper, we study a generalized thin film equation which is relevant to capillary driven flows of thin films of power-law fluids. We prove that the generalized thin film equation in dimension d ≥ 2 has a unique C^1 source type radial self-similar nonnegative solution if 0 〈 n 〈 2p - 1 and has no solution of this type if n ≥ 2p - 1.     

Note on the Blow-up Set for A Semilinear Parabolic Differential System

ＮｏｔｅｏｎｔｈｅＢｌｏｗ－ｕｐＳｅｔｆｏｒＡＳｅｍｉｌｉｎｅａｒＰａｒａｂｏｌｉｃＤｉｆｆｅｒｅｎｔｉａｌＳｙｓｔｅｍ￥ＣｈｅｎＦｕｊｕｎ（陈富均）（ＳｈａｎｇＱｉｕＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ４７６０００）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｎｏｔｅｄ...     

一类具大初值的半线性抛物方程组的生存跨度

The paper deals with heat equations coupled via exponential nonlinearities. We are interested in the life span(or blow-up time) and obtain the maximal existence time of blow-up solutions. Our proof is based on the comparison principle and Kaplan’s method.     

一类半线性积分微分方程初边值问题的爆破解和全局解

本文研究初边值问题的爆破解和全局解，证明了在ｆ的凸性假设和一定的增长性假定下解在有限时刻爆破，而在ｆ的其他假设下证明了全局解的存在性。     

Existence and Orbital Stability of Solitary-Wave Solutions for Higher-Order BBM Equations

This paper discusses the existence and stability of solitary-wave solutions of a general higher-order Benjamin-Bona-Mahony (BBM) equation, which involves pseudo-differential operators for the linear part. One of such equations can be derived from water-wave problems as second-order approximate equations from fully nonlinear governing equations. Under some conditions on the symbols of pseudo-differential operators and the nonlinear terms, it is shown that the general higher-order BBM equation has solitary-wave solutions. Moreover, under slightly more restrictive conditions, the set of solitary-wave solutions is orbitally stable. Here, the equation has a nonlinear part involving the polynomials of solution and its derivatives with different degrees (not homogeneous), which has not been studied before. Numerical stability and instability of solitary-wave solutions for some special fifth-order BBM equations are also given.     

Asymptotic Properties for a Semilinear Edge-Degenerate Parabolic Equation

The author deals with a semi-linear edge-degenerate parabolic equation, and proves that the solution increases exponentially under the initial energy J(u₀) ≤ d, where d is the mountain-pass level. Moreover, the author estimates the blow-up time and the blow-up rate for the solution under J(u₀) < 0.