某类一阶非线性双曲型方程的Cauchy问题

本文考虑一类具实际物理背景的一阶非线性双曲型方程，证明了解的存在唯一及正则性。     

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...     

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).     

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)。     

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.     

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. …     

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.     

THE RIEMANN PROBLEM FOR THE NONLINEAR DEGENERATE WAVE EQUATIONS

In this paper we consider the Riemann problem for the nonlinear degenerate wave equations. This problem has been studied by Sun and Sheng, however the so-called degenerate shock solutions did not satisfy the R-H condition. In the present paper, the Riemann solutions of twelve regions in the v u plane are completely constructed by the Liu-entropy condition. Our Riemann solutions are very different to that one obtained by Sun and Sheng in some regions.     

QUENCHING PROBLEM IN SOME SEMILINEAR WAVE EQUATIONS

This article proves a quenching result of the solutions for some semi-linear wave equations.     

UNIQUENESS OF GENERALIZED SOLUTION FOR THE CAUCHY PROBLEM OF TRANSPORTATTION EQUATIONS

1IntroductionInthepresentpaper,weconsidertheuniquenessofsolutionforthetransportationsystemwithinitialdatawherepanduaredensityandvelocityrespectively.Thesystemofcollservationlaws(1.l)describesthefluidmechanicswithconstantpressure,whichisusedinplasmaphysicswhosepressureisassumedtobeconstant.TheCauchyproblemforthissystemisnotwell-posedintheclassofboundedmeasurablefunctions(see[31).In[8],Z.Wang,F.HuangandX.DinghaveprovedtheealstenceofsolutionsdefinedbyLebesgue--Stieltjesintegral.Beforedetaildi…     

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…     

THE SOLUTION OF THE CAUCHY PROBLEM FOR A WAVE EQUATION WITH VARIABLE COEFFICIENTS

Let \[{\mathfrak{M}_k}\] denote the space of Lorentz witb. constant curvature: \[1 + {K_{\eta pq}}{x^p}{x^q}\] where K is a constant and \[\eta = ({\eta _{pq}})\]=diag [1,... 1,-1], We have considered the wave equation with variable coefficients \[\frac{\partial }{{\partial {x^j}}}(\sqrt {|\tilde g|} ){{\tilde g}^{jk}}\frac{{\partial u}}{{\partial {x^k}}}) = 0\] in \[{\mathfrak{M}_k}\] where \[|\tilde g| = |1 + {K_{\eta pq}}{x^p}{x^q}{|^{ - (n + 1)}},{{\tilde g}^{jk}} = (1 + {K_{\eta pq}}{x^p}{x^q})({\eta _{jk}} + K{x^j}{x^k})\] and found the explicit solution of the Cauchy problem for equation (1)     

THE UNIQUENESS AND CONTINUOUS DEPENDENCE FOR CHARACTERISTIC CAUCHY PROBLEM OF PARTIAL DIFFERENTIAL EQUATIONS

ＴＨＥＵＮＩＱＵＥＮＥＳＳＡＮＤＣＯＮＴＩＮＵＯＵＳＤＥＰＥＮＤＥＮＣＥＦＯＲＣＨＡＲＡＣＴＥＲＩＳＴＩＣＣＡＵＣＨＹＰＲＯＢＬＥＭＯＦＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＬｕａｎＷｅｎｇｕｉ（栾文贵）（ＣｏｍｐｕｔｉｎｇＣｅｎｔ...     

一般非线性扩散方程Cauchy问题广义解的渐近性质

本文研究了比较一般的非线性扩散方程的Cauchy问题广义解的渐近性质.利用试验函数与积分估计的方法,获得了广义解当t→∞时的渐近性质以及其广义整体解u(x,t),推广了该类方程Cauchy问题广义解的性质.     

粘性浅水方程柯西问题解的Lp-估计

本文通过对相应线性方程格林函数的估计，而获得粘性浅水方程柯西问题解的Lp渐近估计。     

奇异半线性非局部反应扩散方程Cauchy问题局部解的存在性

本文讨论如下初值问题局部解的存在性 u/ t- (1/ tσ)Δu =(∫RNuλ(t,y) dy) p /λur + f (x) ,t>0 ,x∈ RNlimt→ 0 + u(t,x ) =0 ,　　　　　　　　　　　　　 x∈ RN其中σ>0 ,λ≥ 1,p≥ 0 ,r≥ 1,p+ r>1,f (x)连续有界非负但不恒等于零 ,Δ是 N维 L aplace算子 ,所得结论推广了文献 [2 ,3]的相应结果     

THE CAUCHY PROBLEM FOR NONHOMOGENEOUS NAVIER-STOKES EQUATIONS IN L~q([0,T];L~p)

1.IntroductionInthispaperweconsiderCauchyproblemforaclassofnonhomogeneousNavier-Stokesequationsintheinfinitecylinderwith.Givensatisfyinginthedistributionsensediv,weseekasolutionvectorandapressurefunctionP(t,x)suchthatwhereisanonlinearvector-valuedfun...     

THE EXISTENCE OF GLOBAL SOLUTION AND THE BLOWUP PROBLEM FOR SOME p-LAPLACE HEAT EQUATIONS

This article consider, for the following heat equation ut/|x|s-△pu=uq,(x,t)∈Ω×(0,T), u(x,t)=0,(x,t)∈(?)Ω×(0,T), u(x,0)=u0(x),u0(x)≥0,u0(x)(?)0 the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, whereΩis a smooth bounded domain in RN(N>p),0∈Ω,△pu=div(|▽u|p-2▽u),0≤s≤2,p≥2,p-1相似文献   

一类退化-奇异抛物型方程的行波解Ⅰ

多孔介质动力学方程吸引了众多人的注意,引起了数学家们的极大兴趣.退化-奇异抛物型方程的行波解也成为令人瞩目的问题.Aronson,Hosono,Atkinson,Engler,Grindron 和 Sleeman,Wang 和 Ye 等在这一领域中都有出色的工作.Aronson 对 m=k=1,u~nf(u)∈C~1[0,1],讨论了单调行波解的存在性.Hosono 对m=1,k≥2,n=0,f∈C~2[0,1],f′(0)<0,f″(0)(?)0,f′(1)<0,且存在α∈