共查询到20条相似文献，搜索用时 31 毫秒
1.
The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems
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$\left\{ \begin{gathered}
- \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
- \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
\end{gathered} \right.$\left\{ \begin{gathered}
- \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
- \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
\end{gathered} \right. 相似文献
2.
We consider the first-order Cauchy problem
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$
\begin{gathered}
\partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\
u|_{z = 0} = u_0 , \hfill \\
\end{gathered}
$
\begin{gathered}
\partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\
u|_{z = 0} = u_0 , \hfill \\
\end{gathered}
相似文献
3.
Let L be a self-adjoint linear operator and N be the gradient of a functional ϕ, which is almost quadratic. We first give a theorem on the surjectivity of the operator L+N, then apply the result to semilinear elliptic systems:
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相似文献
4.
Suppose a, b, and are reals with a<b and consider the following diffusion equation |
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5.
The authors consider the well-posedness in energy space of the critical non-linear system of wave equations with Hamiltonian structure{utt-△u=-F1（｜u｜^2,｜v｜^2）u,utt-△u=-F2（｜u｜^2,｜v｜^2）u where there exists a function F（λ,μ） such that δF（λ,μ）/δλ=F1（λ,μ）.δF（λ,μ）/δμ=F2（λ,μ） By showing that the energy and dilation identities hold for weak solution under some assumptions on the non-linearities, we prove the global well-posedness in energy space by a similar argument to that for global regularity as shown in ＂Shatah and Struwe＇s paper, Ann. of Math. 138, 503-518 （1993）＂. 相似文献
6.
The paper is devoted to the study of the behavior of the following mixed problem for large values of time: where Ω is an unbounded region of ℝ
n
with, generally speaking, noncompact boundary
; the surface Γ is star-shaped (relative to the origin), ν is the unit outer normal to ∂Ω; and the initial functions f and g are assumed to be sufficiently smooth and finite. Under certain restrictions on the part of the boundary Γ 2 constrained by the impedance condition, we establish that one can match the impedance g≥0 (characterizing the absorption of energy by the surface Γ 2) to the geometric properties of this surface so that the energy on an arbitrary compact set will decay at a rate characteristic
for the first mixed problem.
Translated from Matematicheskie Zametki, Vol. 66, No. 3, pp. 393–400, September, 1999. 相似文献
7.
A simple qualitative model of dynamic combustion |
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8.
Abstract Let Ω be the unit ball centered at the origin in
. We study the following problem
By a constructive argument, we prove that for any k = 1, 2, • • •, if ε is small enough, then the above problem has positive a solution uε concentrating at k distinct points which tending to the boundary of Ω as ε goes to 0 +. 相似文献
9.
The paper suggests some conditions on the lower order terms, which provide that the solution of the Dirichlet problem for
the general elliptic equation of the second order
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$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
相似文献
10.
A graph G with p vertices and q edges, vertex set V( G) and edge set E( G), is said to be super vertex-graceful (in short SVG), if there exists a function pair ( f, f
+) where f is a bijection from V( G) onto P, f
+ is a bijection from E( G) onto Q, f
+(( u, v)) = f( u) + f( v) for any ( u, v) ∈ E( G), and
We determine here families of unicyclic graphs that are super vertex-graceful.
相似文献
11.
We prove the existence and the uniqueness of a weak solution to the mixed boundary problem for the elliptic-parabolic equation |
1, \hfill \\ \end{gathered} $$
" align="middle" vspace="20%" border="0">
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with a monotone nondecreasing continuous function b. Such equations arise in the theory of non-Newtonian filtration as well as in the mathematical glaciology. Bibliography: 16 titles. 相似文献
12.
Abstract In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions： {ut-a（u, v）△u=g（u, v）, vt-b（u, v）△v=h（u, v）, δu/δη=d（u, v）, δu/δη=f（u, v）.Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques. 相似文献
13.
The initial boundary value problem
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$ {*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ $ \begin{array}{*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ \end{array} 相似文献
14.
This paper is concerned with a nonlocal hyperbolic system as follows utt = △u ＋ （∫Ωvdx ）^p for x∈R^N,t〉0 ,utt = △u ＋ （∫Ωvdx ）^q for x∈R^N,t〉0 ,u（x,0）=u0（x）,ut（x,0）=u01（x） for x∈R^N,u（x,0）=u0（x）,ut（x,0）=u01（x） for x∈R^N, where 1≤ N ≤3, p ≥1, q ≥ 1 and pq 〉 1. Here the initial values are compactly supported and Ω belong to R^N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed. 相似文献
15.
The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate.It follows that the solution converges to the solution of a nonlinear diffusion problem,as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity. 相似文献
16.
It is proved that the boundary-value problem , has a solution, provided that the following conditions are fulfilled: , and, for ϕ(u) ≡ 0, the Galerkin method converges in the norm of the space H 1(a, b; a). Several theorems of a similar kind are presented. Bibliography: 4 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 246–266. 相似文献
17.
Let D be a bounded domain in an n-dimensional Euclidean space Rn. Assume that 0 ＜ λ1 ≤λ2 ≤ … ≤ λκ ≤ … are the eigenvalues of the Dirichlet Laplacian operator with any order l{(-△)lu=λu, in D u=(δ)u/(δ)(→n)=…(δ)l-1u/(δ)(→n)l-1=0,on (δ)D.Then we obtain an upper bound of the (k 1)-th eigenvalue λκ 1 in terms of the first k eigenvalues.k∑i=1(λκ 1-λi) ≤ 1/n[4l(n 2l-2)]1/2{k∑i=1(λκ 1-λi)1/2λil-1/l k∑i=1(λκ 1-λi)1/2λ1/li}1/2.This ineguality is independent of the domain D. Furthermore, for any l ≥ 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang. 相似文献
18.
The solvability of the nonlocal boundary value problem in a class of functions is investigated for a quasilinear parabolic equation. The solution uniqueness follows from the maximum principle. 相似文献
19.
In this paper we consider a class of nonlinear elliptic problems of the type
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$
\left\{ \begin{gathered}
- div(a(x,\nabla u)) - div(\Phi (x,u)) = fin\Omega \hfill \\
u = 0on\partial \Omega , \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
- div(a(x,\nabla u)) - div(\Phi (x,u)) = fin\Omega \hfill \\
u = 0on\partial \Omega , \hfill \\
\end{gathered} \right.
相似文献
20.
This paper is concerned with a class of even order nonlinear damped differential equations where n is even and t≥ t
0. By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which
are either extensions of or complementary to a number of existing results.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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