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.     

A NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO CAUCHY PROBLEM OF QUASILINEAR HYPERBOLIC SYSTEMS IN DIAGONAL FORM

This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form.A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t 0 is obtained,and a sharp estimate of the life span for the classical solution is given.     

GLOBAL SOLUTION TO THE CAUCHY PROBLEM ON A UNIVERSE FIREWORKS MODEL

We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe fireworks is mathematically easy, this article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution by means of methods taken from the famous work by DiPerna ＆ Lions about the Boltzmann equation. We also show both the regularity and the time-asymptotic behavior of solution to the Cauchy problem.     

一类双色散波方程的Cauchy问题

This paper concerns with the Cauchy problem for the nonlinear double dispersive wave equation.By the priori estimates and the method in [9],It proves that the Cauchy problem admits a unique global classical solution.And by the concave method,we give sufficient conditions on the blowup of the global solution for the Cauchy problem.     

Small amplitude solutions of the generalized IMBq equation

In this paper, the global existence of small amplitude solution for the Cauchy problem of the multidimensional generalized IMBq equation is proved. Moreover, we obtain a nonlinear scattering result of the Cauchy problem of the IMBq equation for small initial data.     

ON THE CAUCHY PROBLEM OF TRANSPORTATION EQUATIONS

1.IntroductionInthepreselltpaper,weconsiderthetransportationsystemwithinitialdatawherepanduaredensityandvelocityrespectively.Thesystemofconservationlaws(1.1)describesthefluidmechanicswithconstalltpressuxe,whichisusedinplasmaphysicswherepressureisassumedtobeaconstant.Thissystemisnon--strictlyhyperbolicwithadoubleeigenvalueAl~AZ=albothAl,AZbeinglinearlydegenerate.AndtheCauchyproblemforthissystemisnotwell-posedintheclassofmeasurableandboundedfunctions(see[3]).Inthepresentpaper,weintroduceanew…     

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.     

Global smooth solution of hydrodynamical equation for the Heisenberg paramagnet

In this note, we obtain the existence and uniqueness of global smooth solution for the Cauchy problem of multidimensional hydrodynamical equation for the Heisenberg paramagnet. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

半线性拟双曲型积分微分方程的初边值问题和初值问题

本文讨论半线性拟双曲型积分微分方程的初边值和初值问题。用积分方程的理论和Ｇａｌｅｒｋｉｎ方法证明了问题的整体强解的存在性、唯一性和正则性。     

Global Solutions and Their Large-time Behavior of Cauchy Problem for Equations of Deep Water Type

We consider the large time behavior of the global solution of the Cauchy problem for the equation of Benjamin-Ono type. A series of large-time global estimates for Cauchy problem arc constructed. By means of the obtained global estimates uniformly for 0 ≤ t < ∞, the attractors of the Cauchy problem for the mentioned nonlinear equations are considered. And also the dimensions of the global attractor are estimated.     

阻尼波动方程在模空间上的一些估计

本文研究分数次阻尼波动方程解在模空间上的估计及相应的时空估计, 作为应用, 我们将得到小初值条件下一类Cauchy问题的全局解.     

Global smooth solution for nonlinearly damped p-system with large initial data

In this paper, we prove the existence of global smooth solution for the Cauchy problem of nonlinearly damped p-system with large initial data. The analysis is based on several key a prioriestirmates. which are obtained by the tnaxirnum principle. Our results extend the corresponding results in [l0,11].     

一类N维非线性波动方程的Cauchy问题

证明下列非线性波动方程的Cauchy问题v_(tt)-α△v_(tt)-Δv=g(v)-αΔg(v),x∈R~N,t>0,(1)v(x,0)=v_0(x),v_t(x,0)=v_1(x),x∈R~N(2)在空间C~2([0,∞);H~s(R~N))(s>N/2)中存在唯一整体广义解v和在空间C~2([0,∞);H~s(R~N))(s>2+N/2N)中存在唯一整体古典解v,即u∈C~2([0,∞);C_B~2(R~N)).还证明Cauchy问题(1),(2)在C~3([0,∞);W~(m,p)(R~N)∩L~∞(R~N))(m≥0,1≤p≤∞)中有唯一整体广义解v和在C~3([0,∞);W~(m,p)(R~N)∩L~∞(R~N))(m>2+N/P)中有唯一整体古典解v,即v∈C~3([0,∞);C~2(R~N)∩L~∞(R~N)).     

一类具阻尼非线性波动方程的Cauchy问题

本文研究一类具阻尼非线性波动方程Cauchy问题整体广义解和整体古典解的存在唯一性,并用凸性方法给出解爆破的充分条件.     

GLOBAL EXISTENCE OF WEAKLY DISCONTIN UOUS SOLUTIONS TO THE CAUCHY PROBLEM WITH A KIND OF NON-SMOOTH INITIAL DATA FOR QUASILINEAR HYPERBOLIC SYSTEMS

The authors consider the Cauchy problem with a kind of non-smooth initial datafor quasilinear hyperbolic systems and obtain a necessary and sufficient condition toguarantee the existence and uniqueness of global weakly discontinuous solution.     

饱和Activator-Inhibitor模型柯西问题的整体解

本文首先证明了饱和Activator－Inhibitor模型柯西问题整体解的存在性，其次考虑到Activator对源密度的反馈效应，又证明了具有反馈的上述模型整体解的存在性．     

Global strong solutions for nonhomogeneous heat conducting Navier‐Stokes equations

We study the Cauchy problem of the 3‐dimensional nonhomogeneous heat conducting Navier‐Stokes equations with nonnegative density. First of all, we show that for the initial density allowing vacuum, the strong solution to the problem exists globally if the velocity satisfies the Serrin's condition. Then, under some smallness condition, we prove that there is a unique global strong solution to the 3D viscous nonhomogeneous heat conducting Navier‐Stokes flows. Our method relies upon the delicate energy estimates.     

带线性坍塌项和竞争势的非线性波动方程柯西问题的稳定集和不稳定集(英文)

本文考虑带线性坍塌项和竞争势的非线性波动方程柯西问题,定义了新的稳定集和不稳定集,证明了如果初值进入不稳定集,则解在有限时间爆破;如果初值进入稳定集,则整体解存在.运用势井讨论,回答了当初值在多么小的时候,该柯西问题的整体解存在.     

对角型拟线性双曲组整体经典解的渐近行为

This paper deals with the asymptotic behavior of global classical solutions to quasilinear hyperbolic systems of diagonal form with weakly linearly degenerate characteristic fields. On the basis of global existence and uniqueness of C^1 solution, we prove that the solution to the Cauchy problem approaches a combination of C^1 traveling wave solutions when t tends to the infinity.