ON THE CAUCHY PROBLEM FOR AW-RASCLE SYSTEM WITH LINEAR DAMPING

The existence of global BV solutions for the Aw-Rascle system with linear damping is considered.In order to get approximate solutions we consider the system in Lagrangian coordinates,then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of[1]we get a sequence of approximate solutions.Finally we show the convergence of this approximate sequence to the weak entropic solution.     

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.     

ON THE CAUCHY PROBLEM FOR A SINGULAR INTEGRODIFFERENTIAL EQUATION

The authors establish the existence and uniqueness of global solutions to the Cauchy problem for the third-order Benjamin-Ono equation by the so-called continuation method.     

GLOBALLY SMOOTH SOLUTIONS TO CAUCHY PROBLEM OF A QUASILINEAR HYPERBOLIC SYSTEM ARISING IN BIOLOGY

We consider Cauchy problem of the system of nonlinear conservation lawsut -- (liv). = 0, vf -- uz = 0, (x,t) E R x R , (E)with initial datau(2,0) = u0(2), v(x,0) = v0(x), z E R. (I)It has been 8hown in [1,2],the system (E) describes the maro8copic behaviour of some (so-called"chemOtatic ") bacterial populations, which are attracted by the gradient of some chendcalsubstrate, which they metabolize. When the bacteria have depleted the substrate somewliere,this create8 a gradient in the concen…     

四阶Ginzburg-Landau型方程的初值问题

本文研究四阶Ginzburg-Landau型方程的初值问题,通过建立一般半线性抛物方程的Lr-解和Hs-解之间的联系,获得该方程的整体Hs-解的存在唯一性(s=1,2).     

CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient.For regular initial data,we show that the unique strong s...     

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…     

四阶Ginzburg-Landau型方程的初值问题

本文研究四阶Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ型方程的初值问题,通过建立一般半线性抛物方程的Ｌτ－解和Ｈｓ－解之间的联系,获得该方程的整体Ｈｓ－解的存在唯一性(ｓ＝１、２)。     

THE CAUCHY PROBLEM FOR SOME DISPERSIVE WAVE EQUATIONS

In this paper, we consider the Cauchy problem for some dispersive equations. By means of nonlinear estimate in Besov spaces and fixed point theory, we prove the global well-posedness of the above problem. What‘s more, we improve the scattering result obtained in [1].     

THE CAUCHY PROBLEM FOR A NONLINEAR FAST DIFFUSION EQUATION

In this paper, the existence, uniqueness and continuous dependence on initial data for the Cauchy problem of fast diffusion equation is discussed.     

奇异半线性反应扩散方程组Cauchy问题

本文讨论如下问题其中{(б)u/(б)t-(1/tσ)△u=αvp1+β1vp1+f1(x),t>0,x∈RN,(б)u/(б)t-(1/tσ)△v=α2uq2+β2vp2+f2(x),t>0,∈RN,limt→0+u(t,x)=limt→0+v(t,x)=0,x∈Rn,其中σ＞0,pi＞1,qi＞1(i=1,2),α1≥0,α2＞0,β1＞0,β2≥0,fi(x)(i=1,2)连续有界非负,(f1(x),f2(x))(≡／)(0,0).给出了非负局部解存在的几个充分条件和解的爆破结果.     

ON THE INITIAL VALUE PROBLEM FOR THE BIPOLAR SCHRODINGER-POISSON SYSTEM

In this paper, we prove the existence and uniqueness of global solutions in H^s(R^3) ( s∈R, s≥0) for the initial value problem of the bipolar Schrodinger-Poisson systems.     

一种求解修正的Helmholtz方程Cauchy问题的数值方法

本文研究了无界带形区域Ω={(x,y)|0相似文献   

BLOWUP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEARWAVE EQUATIONS

gi. IntroductionThis paper deals with solutionS of certain nonlinear wave equationS Of the formcorresponding to Antial conditionSwuersis the wave OPerstor.we are interested in showing the ~ up" Of solutions to (1.1)--(1.2). For that, wereIf ac ~ 1)(n ~ 1) > 2, global solutions of ~ equation subject to very general perturbationsof order p exist Provided the initial data are swhciently small (see I6] and references therein).We are also interested in esthaattw the take when "blow up" occurs. …     

奇异半线性反应扩散方程组Cauchy问题

本文讨论如下问题其中σ>0,Pi>1,qi>1(i=1,2),α1≥0,α2>0,β1>0,β2≥0,fi(x)(i=1,2)连续有界非负, (f1(x),f2(x))(?)(0,0).给出了非负局部解存在的几个充分条件和解的爆破结果.     

CAUCHY PROBLEM FOR FRACTIONAL BEAM-LIKE EQUATIONS

In one space-and in one time -dimension a beam-like equation is solved, where the second time derivative is replaced by the a?fractional time derivative, 1 <α< 2. The solution is given in closed form in terms of the Mttag-Leffler functions in two parameters.     

三维Laplace方程Cauchy问题的小波解(英文)

本文研究了三维Laplace方程的柯西问题.该问题是不适定的,即其解(若存在)不连续依赖原始数据.利用Meyer小波和小波Galerkin方法,获得了在L2范数意义下的稳定小波逼近解,并且给出分辨率水平的选取方法.     

Cauchy问题解的不唯一性定理

设P是R~n上常系数m阶齐次线性偏微分算子,m>1,则对于任何给定的正数c、b、ε,下述Cauchy问题 存在非平凡解u,满足     

BLOWUP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEARWAVE EQUATIONS

The author proves blow up of solutions to the Cauchy problem of certain nonlinear wave equations and, also, estimates the time when the blow up occurs.