共查询到20条相似文献,搜索用时 109 毫秒
1.
本文考虑下面的Dirichlet问题ut一Tr[a(x,t)D2u]+H(x,t,u,Du)=0,(x,t)∈QT=Ω×(0,T),u(x,t)=ψ(x,t), (x,t)∈ГT. (DP)利用粘性解理论证明了当H,Г满足一定条件时,(DP)的粘性解u(x,t)满足如果ψ∈Ca2,则u(x,t)∈Cα,羞;若ψ=0,则u(x,t)是Lpschitz连续的. 相似文献
2.
1 引 言考虑下述非线性双曲型方程的混合问题:c(x,u)utt-.(a(x,u)u)=f(x,u,t), x∈Ω,t∈J,(1.1)u(x,0)=u0(x), x∈Ω,(1.2)ut(x,0)=u1(x), x∈Ω,(1.3)u(x,t)=-g(x,t), (x,t)∈Ω×J,(1.4)其中ΩR2是一具有Lipschitz边界Ω的有界区域,J=[0,T],0相似文献
3.
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
4.
方程u_(tt)=u_(xxt)+f(u_x)_x初边值问题的差分法 总被引:10,自引:0,他引:10
The finite difference method is considered for the followinginitial-boundary-value problem: arrayllutt=uxxt+f(ux)x, & (x,t) QT, u(x,0) =(x), & x [0,1], ut(x,0) = (x), & x [0,1], u(0,t) =u(1,t) =0, & t [0,T],array. where f(s),(x) and (x) are given functions;QT=[0,1] [0,T]. The convergence of the finite difference schemesis verified by discrete functional analysis methods and prior estimationtechniques. 相似文献
5.
1引言 关于反应扩散方程的研究由来已久,特别是对一些含参数的非线性反应扩散方程,由于其多解性和丰富的分歧现象,经常受到人们的关注.本文考虑如下非线性反应扩散方程组 {ut=γf(u,v)+uxx, vt=γg(u,v)+dvxx, (1) 相应的边界条件为 ux(t,0):ux(t,π)=vx(t,0)=vx(t,π)=0. (2) 我们选取Gierer-Meinhardt模型[1,2]为研究对象,即 {f(u,V)=a-bu+u2/v, g(u,v)=u2-v, 其中a、b和γ是正常数,d为参数. 相似文献
6.
1.引言 本文考察以下奇异摄动转向点问题: Lu≡ε~2u″+xa(x)u′-b(x)u=f(x),x∈I=[-1,1], u(-1)=A,u(1)=B, (1.1)其中参数ε是(0,1]中的常数,函数a(x)∈C~3[I],b(x),f(x)∈C~4[I]且满足a(x)≥a_*>0,b(x)≥b_*>0.在以上假设下,由[1]知,方程(1.1)存在唯一解u_8∈C~5[I]且 相似文献
7.
本文讨论了带非均匀项的MKdV方程:ut 6u^2ux uxxx βu (α βx)ux=0(1.1)它与特征值问题Vx=QV(1.3)相联系,文章推导了方程(1.3)的散射数据的演化规律,得到了方程(1.1)的反散射解-孤子解。最后还讨论了单孤子解和双孤子解。 相似文献
8.
针对双曲型方程定解问题{utt=a2uxx+f(t),0xπ,a∈R且a≠0,u(0,t)=v1(t),u(π,t)=v2(t),t0,u(x,0)=g(x),ut(x,0)=h(x),0≤x≤π研究了可以唯一决定未知函数组{v1(t),v2(t),f(t)}的基本条件,提出了该定解问题的反问题,并且讨论了此反问题的存在性与唯一性. 相似文献
9.
10.
关于双曲型偏微分方程 u_(xy)=f(x,y,u,u_x,u_y),0≤x≤a,0≤y≤b,-∞相似文献
11.
Let $p>1$ . We study the behavior of certain positive and nodal solutions of the problem $$\begin{aligned} \left\{ \,\, \begin{array}{lll} -\Delta _p u=\lambda |u|^{q-2}u \ \ &{}\mathrm{in} \ \ &{}{\varOmega } \\ u=0 &{}\mathrm{in} \ \ &{}\partial {\varOmega } \end{array}\right. \end{aligned}$$ on varying of the parameters $\lambda >0$ and $q>1$ . 相似文献
12.
ONTHEBOUNDEDANDUNBOUNDEDSOLUTIONSOFONEDIMENSIONALNONLINEARREACTION-DIFFUSIONPROBLEM¥GEWEIGAOR.O.WEBERAbstract:Theexistenceofb... 相似文献
13.
Giovanna Cerami Mónica Clapp 《Calculus of Variations and Partial Differential Equations》2007,30(3):353-367
We prove the existence of a sign changing solution to the semilinear elliptic problem , in an exterior domain Ω having finite symmetries. 相似文献
14.
We study the large time behavior of the solutions of the Cauchy problem for a semilinear heat equation,
$\partial_t u=\Delta u+F(x,t,u) \quad{\rm in}
\;{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad{\rm in}
\;{\bf R}^N,\quad\quad ({\rm P})$\partial_t u=\Delta u+F(x,t,u) \quad{\rm in}
\;{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad{\rm in}
\;{\bf R}^N,\quad\quad ({\rm P}) 相似文献
15.
Relja Vulanovic 《计算数学(英文版)》1991,9(4):321-329
We consider the singular perturbation problem $$-\varepsilon^2u"+\mu b(x,u)u'+c(x,u)=0,u(0),u(1)$$ given with two small parameters $\varepsilon$ and $\mu$ , $\mu =\varepsilon^{1+p},p>0$. The problem is solved numerically by using finite difference schemes on the mesh which is dense in the boundary layers. The convergence uniform in $\varepsilon$ is proved in the discrete $L^1$ norm. Some convergence results are given in the maximum norm as well. 相似文献
16.
Let B R~n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ* 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r~(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] . 相似文献
17.
Giovanni Anello 《Monatshefte für Mathematik》2011,185(2):1-18
We study the behavior of positive solutions of the following Dirichlet problem
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