共查询到20条相似文献,搜索用时 9 毫秒
1.
Zheng Songmu 《数学年刊B辑(英文版)》1983,4(4):443-462
The initial bounary value problem for quasilinear byperbolie-parabolic coupled systems in higher dimensional spaces, which arises in many mechanical problerns is considered. Under the assumptions that the-hyperbolic part of the coupled system is a quasilinear symmetric hyperbolic system and the parabolic part is a quasilinear parabolic system of second order and suitable assumptions of smoothness and compatibiliy conditions, the existence and uniqueness of local smooth solution is proved in the cases that the boundary of domain is noncharacteristic or uniformly characteristic with respect to the hyperbolic part.
As an application, the existence and uniqueness of local smooth solution for the initial boundary problem of the radiation hydrodynamic system, as well as of the viscous compressible hydrodynamic system, with solid wal1 boundary, is obtained. 相似文献
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通过推广上下解的概念,利用上下解方法讨论了二阶微分系统-x″(t)=f(t,x)分别在边值条件x(0)=0,x′(1)=0和x(0)=A,x(1)=B下解的存在性. 相似文献
3.
本文讨论了一类二阶拟线性微分方程的奇摄动问题 .在适当的条件下 ,本文用一种新的方法分析了原问题解的存在性、唯一性及渐近性态 . 相似文献
4.
The Nonlinear Boundary Value Problems of Three Elements for the First Order Quasilinear Elliptic Systems 下载免费PDF全文
Hu Guoen 《偏微分方程(英文版)》1992,5(1)
In this paper, we discuss the nonlinear boundary value problems of three elements with two shifts for the first order quasilinear elliptic systems and the related solvability by using the continuity method. 相似文献
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The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle. 相似文献
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当非线性项奇异和无穷远处的极限增长函数存在时,考察了一类二阶拟线性边值问题.通过引入非线性项在有界集合上的高度函数,并且考察高度函数的积分,证明了一个解的存在定理.该定理表明当极限增长函数的积分具有适当值时此问题有一个解. 相似文献
7.
运用不动点指数理论,讨论了用P-Laplacian算子研究奇异边值问题正解的存在性.作为其应用,给出了一个例子. 相似文献
8.
该文研究一类非线性高阶波动方程utt-a1Uxx+a_2ux4+a3ux4tt=φ(ux )x+f(u,ux,uxxuxxx,ux4)的初边值问题.证明整体古典解的存在唯一性并给出古典解爆破的充分条件. 相似文献
9.
利用先验估计的方法讨论具非线性第二边界条件的快扩散方程解的存在性、唯一性、稳定性和渐近性.主要结果是:1)存在唯的整体广义解,解连续依赖于初值;2)存在T0,t<T0时解是无穷次可微的正则解;3)当t充分大时,解一致收敛到零. 相似文献
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We introduce symmetric Boundary Value Methods for the solution of second order initial and boundary value problems (in particular
Hamiltonian problems). We study the conditioning of the methods and link it to the boundary loci of the roots of the associated
characteristic polynomial. Some numerical tests are provided to assess their reliability.
Dedicated to the memory of Professor Aldo Cossu 相似文献
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The Nonlinear Singularly Perturbed Initial Boundary Value Problems of Nonlocal Reaction Diffusion Systems 总被引:7,自引:0,他引:7
Jia-qi Mo Wan-tao Lin 《应用数学学报(英文版)》2006,22(2):277-286
In this paper the singularly perturbed initial boundary value problems for the nonlocal reactiondiffusion system are considered.Using the iteration method and the comparison theorem,the existence and itsasymptotic behavior of the solution for the problem are studied. 相似文献
14.
Liang Zhongchao 《数学年刊B辑(英文版)》1982,3(1):79-84
In this paper, the existence and uniqueness of solution of the limit boundary value problem
$\[\ddot x = f(t,x)g(\dot x)\]$(F)
$\[a\dot x(0) + bx(0) = c\]$(A)
$\[x( + \infty ) = 0\]$(B)
is considered, where $\[f(t,x),g(\dot x)\]$ are continuous functions on $\[\{ t \ge 0, - \infty < x,\dot x < + \infty \} \]$ such that the uniqueness of solution together with thier continuous dependence on initial value are ensured, and assume: 1)$\[f(t,0) \equiv 0,f(t,x)/x > 0(x \ne 0);\]$; 2) f(t,x)/x is nondecreasing in x>0 for fixed t and non-increasing in x<0 for fixed t, 3)$\[g(\dot x) > 0\]$,
In theorem 1, farther assume: 4) $\[\int\limits_0^{ \pm \infty } {dy/g(y) = \pm \infty } \]$
Condition (A) may be discussed in the following three cases
$x(0)=p(p \neq 0)$(A_1)
$\[x(0) = q(q \ne 0)\]$(A_2)
$\[x(0) = kx(0) + r{\rm{ }}(k > 0,r \ne 0)\]$(A_3)
The notation $\[f(t,x) \in {I_\infty }\]$ will refer to the function f(t,x) satisfying $\[\int_0^{ + \infty } {\alpha tf(t,\alpha )dt = + \infty } \]$ for each $\alpha \neq 0$,
Theorem. 1. For each $p \neq 0$, the boundary value problem (F), (A_1), (B) has a solution if and only if $f(t,x) \in I_{\infty}$
Theorem 2. For each$q \neq 0$, the boundary value problem (F), (A_2), (B) has a solution if and only if $f(t, x) \in I_{\infty}$.
Theorem 3. For each k>0 and $r \neq 0$, the boundary value problem (F), (A_3), (B) has a solution if and only if f(t, x) \in I_{\infty},
Theorem 4. The boundary value problem (F), (A_j), (B) has at most one solution for j=l, 2, 3. . 相似文献
15.
本文利用Leray-Schauder不动点定理证明了非线性波方程utt-[a0 a2(ux)^β]uxx-a1uxxtt=f(x,t,ux,ut,uxt)的初边值问题广义解的存在唯一性。 相似文献
16.
In this paper, the Nagumo theorem and the fixed-point theorem are used to prove the existence and the uniqueness and to estimate the asymptotic expansion of the shock solutions of the boundary value problems for a class of quasilinear differential equations, the asymptotic expansion of solution of any orders including boundary is obtained. 相似文献
17.
本文研究一类在球内的非线性椭圆奇异边值问题的正解的存在性,推广了H.Usami1989年所得到的部分结果 相似文献
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非线性奇异扩散方程的第二初边值问题 总被引:2,自引:0,他引:2
讨论了非线性奇异扩散方程的第二初边值问题,证明了存在唯一的光滑解,且解关于初值是连续依赖的.同时还简洁地得到解的渐近性质:tl|u-u0|→0,0<l<1/2. 相似文献
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