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古典解     
相关语句
  classical solution
     Then we study the blow-up of classical solution u(x,t) of problem(1.1)~(1.3) i.e.there exists T_0≤(1+λ_0)∫~∞_αg~(-1)(s)ds such that(lim)t→T~-_0‖u‖_p=∞ for 1≤p≤∞.
     研究了(1.1)~(1.3)的古典解u(x,t)的blow-up性,即存在T0≤(1+λ0)∫α∞g-1(x)ds使得limt→T0-‖u‖p=∞对1≤p≤∞.
短句来源
     The blow-up of classical solution of the initial boundary problem for semilinear pseudoparabolic equations is studied u_t-Δu_t=f(u),x∈Ω,t>0(1.1) u(x,0)=u_0(x),x∈Ω(1.2) u|_(Ω)=0,t≥0(1.3) we discuss the existence of positive solution.
     研究了半线性拟抛物方程的初边值问题ut-Δut=f(u)x∈Ω,t>0(1.1)u(x,0)=u0(x),x∈Ω(1.2)u|Ω=0,t≥0(1.3)古典解的blow-up性. 讨论了正解的存在性.
短句来源
     Global Classical Solution of Schrdinger-Poisson Problem
     Schrdinger-Poisson问题的整体古典解
短句来源
     In the second chapter,we will study the existence and uniqueness of the global generalized solution and the global classical solution to the initial boundary value problem for a class of linear evolutionary equation.
     第二章研究一类线性发展方程的初边值问题的整体广义解和整体古典解的存在性与唯一性; 第三章研究相应的非线性发展方程的初边值问题的局部广义解的存在性与唯一性;
短句来源
     For a class of more general elliptic Monge-Ampère operators raised by Caffarelli-Nirenberg-Spruck,the corresponding parabolic Monge-Ampère equation was studied,the existence and uniqueness of the classical solution to the first boundary-initial value problem for the equation were established,which extended a result of Monge-Ampère equation described by Ladyzhenskaya-Ivochkina.
     对于Caffarelli-N irenberg-Spruck提出的一种更一般的椭圆型Monge-Ampère算子,讨论了相应的抛物型Monge-Ampère方程第一初边值问题,证明了古典解的存在惟一性,推广了Ladyzhenskaya-Ivochkina关于相应抛物型Monge-Ampère方程的结果.
短句来源
更多       
  classical solutions
     Global W~(k,p)(k≥3,1classical solutions of semilinear pseudoparabolic equations
     半线性拟抛物方程的整体W~(k,p)(k≥3,1古典解
短句来源
     The existence and uniqueness of the local classical solutions for the firest initial boundary value problem of the nonliner wave equations of fourth order u_u-[a_0+na_1(u_2)~(n-1)u_(xx)-a_2u_(xx#)=0 are proved by the method of Galerkim.
     本文用Galerkin方法和能量估计,证明了一类四阶非线性波动方程 u_u-[a_0+na_1(u_z)~(n-1)]u_(xx)-a_2u(?) =0的第一初边值问题局部古典解的存在唯一性。
短句来源
     Some sufficient conditions for the existence of positive classical solutions of a singular nonlinear Dirichlet problem,is given.
     应用奇异非线性Dirichlet问题的上下解方法以及极大值原理,得到了一类奇异非线性Dirichlet问题正古典解的存在性.
短句来源
     In this paper the blow-up of Classical solutions of the initial boundary value problem for semilinear pseudoparabolic equations is studied, the results which are similar to but different from the corresponding results of semilinear parabolic equations are obtained.
     本文研究半线性拟抛物方程的初边值问题古典解的blow-up问题,得到了与半线性抛物方程相类似,但又不同的结果.
短句来源
     The Existence of Classical Solutions for a Class of Parabolic Equation with Strong Nonlinearity and Degeneration
     一类具强非线性退化抛物方程古典解的存在性
短句来源
更多       
  classic solution
     The Well-Posed Problems of The Classic Solution of Water Vapour Equation
     水汽方程古典解的适定性研究
短句来源
     This paper studies the existence and structure of the Cauchy problem′s classic solution of the Smoluchowski Equation under the Onsager Potential.
     研究在 Onsager势下 Smoluchowski方程 Cauchy问题的古典解的存在性及其结构 .
短句来源
     At last, it was proven that the classic solution of water vapour equation is non-negative.
     此外 ,还严格证明了水汽方程古典解的非负性
短句来源
     Under the condition of classic solution, the boundary value problem, variation problem and variation equation are equivalent.
     在古典解的条件下,边值问题、变分问题和变分方程是等价的;
短句来源
  the classical solution
     For a class of more general elliptic Monge-Ampère operators raised by Caffarelli-Nirenberg-Spruck,the corresponding parabolic Monge-Ampère equation was studied,the existence and uniqueness of the classical solution to the first boundary-initial value problem for the equation were established,which extended a result of Monge-Ampère equation described by Ladyzhenskaya-Ivochkina.
     对于Caffarelli-N irenberg-Spruck提出的一种更一般的椭圆型Monge-Ampère算子,讨论了相应的抛物型Monge-Ampère方程第一初边值问题,证明了古典解的存在惟一性,推广了Ladyzhenskaya-Ivochkina关于相应抛物型Monge-Ampère方程的结果.
短句来源
     To Y(0)∈, the closed loop system has a unique mild solution, and has a unique classical solution to Y(0)∈D(. The classical solution along the closed loop of the total energy function E(t) of flexible robot arms system attenuates gradually to zero, that is the closed loop system is asymptotic global stable.
     闭环系统对Y(0)∈ H有惟一mild解,对 Y(0)∈D( A有惟一古典解;柔性臂系统的总能量函数E(t)沿闭环系统的古典解渐近衰减到零,即闭环系统具有全局渐近稳定性。
短句来源
     THE CLASSICAL SOLUTION FOR NONLINEAR ELLIPTIC EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS
     非局部非线性椭圆型方程的古典解定理
短句来源
     EXISTENCE OF THE CLASSICAL SOLUTION OF A TWO PHASE STEFAN-SIGNORINI PROBLEM
     一个二相Stefan-Signorini问题古典解的存在性
短句来源
     Observing the relation between this equation and the wave equation, we prove the uniqueness of the classical solution.
     利用它与波方程之间的关系,我们用一个等式变换证明了其古典解的唯一性,并证明了其Cauchy问题光滑解的存在性和唯一性。
短句来源
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      classical solution
    The local existence and uniqueness of classical solution are established.
          
    Global classical solution of free boundary problem for a coupled system
          
    The global classical solution of the problem with free boundary Γ:y=g(x,t) between two domains is under search.
          
    The existence and uniqueness of a nonnegative classical solution are proved.
          
    And some sufficient conditions to ensure the global existence and nonexistence of nonnegative classical solution to this problem are given.
          
    更多          
      classical solutions
    In this case there could be infinitely many functions that are "weak" but not classical solutions.
          
    In this paper, we prove the existence theorems of locbal or global classical solutions to Stefan problems with various kinetic conditions at the free boundary.
          
    In this paper the nonnegative classical solutions of a parabolic system with nonlinear boundary conditions are discussed.
          
    Breakdown of classical solutions to quasilinear hyperbolic systems
          
    In this paper, we show that the Lax connections can yield new classical solutions with a spectral parameter of the hybrid formulism for the Type IIB superstring in an AdS2 × S2 background with Ramond-Ramond flux.
          
    更多          
      classic solution
    The stochastic method, which was formulated earlier by Gurevich and Kharkats on the basis of a classic solution of the Fokker-Planck equation in a phase space of coordinates and momenta, is developed to extend it to the case of intermediate damping.
          
    Existence and uniqueness of the classic solution to a two-dimensional quasistationary Stefan problem are considered.
          
    We show that, in each odd dimensionn =m2, there is a class of Grassmann quotient spaces not included in Wolf's classic solution of the Grassmann space form problem.
          
    The first element captures the combined effect of willingness to pay and marginal cost, i.e., the classic solution after Ramsey (1927).
          
    A sensitive, directional ground varmetric element is the classic solution to ground fault detection in ungrounded systems.
          
    更多          
      the classical solution
    Some general properties of the perturbation spectrum are found and a solution, which includes the classical solution in the absence of turbulence as a limiting case, is obtained.
          
    The main result of our paper is a proof of the uniqueness of the classical solution of a mixed problem for a second-order hyperbolic equation in a normal cylinder.
          
    Proof of uniqueness and membership in W21 of the classical solution of a mixed problem for a self-adjoint hyperbolic equation
          
    Furthermore, it is proved that the classical solution of the indicated mixed problem, whenever it exists, belongs to the class W21 and is the generalized solution from W21 of the same problem.
          
    We prove existence and uniqueness theorems for the generalized and the classical solution of the Cauchy problem for this system of equations.
          
    更多          


    Consider the Cauchy problem for the wave equation in n-dimensional

    本文利用λ——阶导数(1/2<λ<1)的嵌入定理改进С.Л.索伯列夫关于n维空间波动方程Cauchy问题解的存在性定理为:如果初始数据u_0∈W_2~(([n/2]+2)H~λ(G))u_1∈W_2~(([n/2]+2)H~λ(G)),(1/2<λ<1),则存在唯一古典解

    In this paper we consider the Cauchy problem for the system of gas dynamics with a viscosity term u_i+[p(v)]_x=μu_(xx),v_t-u_x=0. By means of the theory of nonlinear semigroups, we have proved the existence and uniqueness of the generalized solution of this problem. It follows from the Sobolev imbedding theorems that the generalized solution is in fact classical solution provided the initial data and the function p(v) are appropriate smoothness.

    本文讨论的是具粘性项一维气体动力学方程组u_t+[p(u)]_x=μu_(xx),v_t-u_x=0的Cauchy问题。利用非线性半群的理论作为工具,给出了该Cauchy问题广义解的存在性与唯一性。适当地提高初值u_0(x),v_0(x)及函数p(v)的光滑性,该问题的广义解便是古典解

    In This paper we consider a class of operators with multiple characteristics:Generally P(x,D) = L 'L(x,D) +C where L is a operator which has no solutions. We conclude that the lower order terms, including the zero order term, influence essentially the local solvability, the principal part of p(x,D) is a solvable operator in a neighbourhood of origin, p(x,D) isn't solvable when C = 0, and p(x,D) becomes again solvable when C>0. We also discuss rpyiliHH operator with zero term. Finally, we prove that if the nonhomogeneous...

    In This paper we consider a class of operators with multiple characteristics:Generally P(x,D) = L 'L(x,D) +C where L is a operator which has no solutions. We conclude that the lower order terms, including the zero order term, influence essentially the local solvability, the principal part of p(x,D) is a solvable operator in a neighbourhood of origin, p(x,D) isn't solvable when C = 0, and p(x,D) becomes again solvable when C>0. We also discuss rpyiliHH operator with zero term. Finally, we prove that if the nonhomogeneous term f(x1, is a real function), there are solutions if and only if is analytic.

    本文给出一类型如P(x,D)=D_1~4+x_1~4D_2~4-(i~(1/2)+(-i)~(1/2))D_1~2D_2+4x_1D_1D_2~2-i(i~(1/2)-(-i)~(1/2))x_1~2D_2~3+(1+2i)D_2~2+C 或更一般地p(x,D)=L~tL(x,D)+C(L为无解算子)的多重特征算子。指出包括零阶项在内的低阶项对局部可解性能具有决定性影响。具体地说,在原点邻域上面所给算子p(x,D)的主部D_1~4+x_1~4D_2~4为可解算子,当C=0时P(x,D)为不可解算子。但当C>0时又变为局部可解算子。类似地讨论了算子附加零阶项的一些情况。文章最后证明了当自由项f具形|x_1|ψ'(x_2)(ψ为实函数)时,在原点邻域有古典解的充要条件为ψ(x_2)解析。

     
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