首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 15 毫秒
1.
We establish a priori bounds for positive solutions of semilinear elliptic systems of the form
where Ω is a bounded and smooth domain in . We obtain results concerning such bounds when f and g depend exponentially on u and v. Based on these bounds, existence of positive solutions is proved. Dedicated to Felix Browder on the occasion of his 80th birthday  相似文献   

2.
The purpose of this paper is to characterize all matroids M that satisfy the following minimax relation: for any nonnegative integral weight function w defined on E(M),
Our characterization contains a complete solution to a research problem on 2-edge-connected subgraph polyhedra posed by Cornuéjols, Fonlupt, and Naddef in 1985, which was independently solved by Vandenbussche and Nemhauser in Vandenbussche and Nemhauser (J. Comb. Optim. 9:357–379, 2005). W. Zang’s research partially supported by the Research Grants Council of Hong Kong.  相似文献   

3.
Let H (t, x, p) be a Hamiltonian function that is convex in p. Let the associated Lagrangian satisfy the nonstandard minorization condition where m > 0, ω > 0, and C ≥ 0 are constants. Under some additional conditions, we prove that the associated value function is the unique viscosity solution of S t + H(t, x, ∇S) = 0 in , without any conditions at infinity on the solution. Here ωT < π/2. To the Hamilton–Jacobi equation corresponding to the classical action integrand in mechanics, we adjoin the continuity equation and establish the existence and uniqueness of a viscosity–measure solution (S, ρ) of
This system arises in the WKB method. The measure solution is defined by means of the Filippov flow of ∇S.   相似文献   

4.
We investigate the boundary growth of positive superharmonic functions u on a bounded domain Ω in , n ≥ 3, satisfying the nonlinear elliptic inequality
where c >  0, α ≥ 0 and p >  0 are constants, and is the distance from x to the boundary of Ω. The result is applied to show a Harnack inequality for such superharmonic functions. Also, we study the existence of positive solutions, with singularity on the boundary, of the nonlinear elliptic equation
where V and f are Borel measurable functions conditioned by the generalized Kato class.  相似文献   

5.
This paper is concerned with the large time behavior of traveling wave solutions to the Cauchy problem of generalized Benjamin–Bona–Mahony–Burgers equations
with prescribed initial data
Here v( > 0), β are constants, u  ±  are two given constants satisfying u + ≠ u − and the nonlinear function f(u) ∈C 2(R) is assumed to be either convex or concave. An algebraic time decay rate to traveling waves of the solutions of the Cauchy problem of generalized Benjamin-Bona-Mahony-Burgers equation is obtained by employing the weighted energy method developed by Kawashima and Matsumura in [6] to discuss the asymptotic behavior of traveling wave solutions to the Burgers equation. revised: May 23 and August 8, 2007  相似文献   

6.
This report studies an abstract approach to modeling the motion of large eddies in a turbulent flow. If the Navier-Stokes equations (NSE) are averaged with a local, spatial convolution type filter, , the resulting system is not closed due to the filtered nonlinear term . An approximate deconvolution operator D is a bounded linear operator which is an approximate filter inverse
Using this general deconvolution operator yields the closure approximation to the filtered nonlinear term in the NSE
Averaging the Navier-Stokes equations using the above closure, possible including a time relaxation term to damp unresolved scales, yields the approximate deconvolution model (ADM)
Here , χ ≥ 0, and w * is a generalized fluctuation, defined by a positive semi-definite operator. We derive conditions on the general deconvolution operator D that guarantee the existence and uniqueness of strong solutions of the model. We also derive the model’s energy balance. The author is partially supported by NSF grant DMS 0508260.  相似文献   

7.
We study the existence and uniqueness of solutions of the convective–diffusive elliptic equation
posed in a bounded domain , with pure Neumann boundary conditions
Under the assumption that with p = N if N ≥ 3 (resp. p > 2 if N  =  2), we prove that the problem has a solution if ∫Ω f dx  = 0, and also that the kernel is generated by a function , unique up to a multiplicative constant, which satisfies a.e. on Ω. We also prove that the equation
has a unique solution for all ν > 0 and the map is an isomorphism of the respective spaces. The study is made in parallel with the dual problem, with equation
The dependence on the data is also examined, and we give applications to solutions of nonlinear elliptic PDE with measure data and to parabolic problems.  相似文献   

8.
In this paper we prove the L ∞-boundedness of solutions of the quasilinear elliptic equation
$ {ll} Au \, = f(x,u,\nabla u) &\quad \rm{in }\, \Omega, \\ \dfrac{\partial u}{ \partial \nu} \, = g(x,u) &\quad \rm{on }\, \partial \Omega, $ \begin{array}{ll} Au \, = f(x,u,\nabla u) &\quad \rm{in }\, \Omega, \\ \dfrac{\partial u}{ \partial \nu} \, = g(x,u) &\quad \rm{on }\, \partial \Omega, \end{array}  相似文献   

9.
We consider autonomous integrals
in the multidimensional calculus of variations, where the integrand f is a strictly W 1,p -quasiconvex C 2-function satisfying the (p,q)-growth conditions
with exponents 1 < p ≤  q < ∞. Under these assumptions we establish an existence result for minimizers of F in provided . We prove a corresponding partial C 1,α -regularity theorem for . This is the first regularity result for autonomous quasiconvex integrals with (p,q)-growth.  相似文献   

10.
We consider the Allen–Cahn equation
where Ω is a smooth and bounded domain in such that the mean curvature is positive at each boundary point. We show that there exists a sequence ε j → 0 such that the Allen–Cahn equation has a solution with an interface which approaches the boundary as j → + ∞.  相似文献   

11.
Countable families of global-in-time and blow-up similarity sign-changing patterns of the Cauchy problem for the fourth-order thin film equation (TFE-4)
$u_t=-\nabla \cdot \left(|u|^n \nabla \Delta u\right) \quad {\rm in} \quad \mathbb{R}^{N}\times\mathbb{R}_{+} \quad{\rm where}\quad n >0 ,$u_t=-\nabla \cdot \left(|u|^n \nabla \Delta u\right) \quad {\rm in} \quad \mathbb{R}^{N}\times\mathbb{R}_{+} \quad{\rm where}\quad n >0 ,  相似文献   

12.
We consider the mixed problem,
in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data, f D , has one derivative in L p (D) of the boundary and the Neumann data, f N , is in L p (N). We find a p 0 > 1 so that for p in an interval (1, p 0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L p . L. Lanzani, L. Capogna and R. M. Brown were supported, in part, by the U.S. National Science Foundation.  相似文献   

13.
We consider the overdetermined eigenvalue problem on a sufficiently regular connected open domain Ω on the 2-sphere :
where α ≠ 0. We show that if α = 2 and Ω is simply connected then the problem admits a (nonzero) solution if and only if Ω is a geodesic disk. We furthermore extend to domains on the isoperimetric inequality of Payne–Weinberger for the first buckling eigenvalue of compact planar domains. As a corollary we prove that Ω is a geodesic disk if the above overdetermined eigenvalue problem admits a (nonzero) solution with ∂u/∂ν = 0 on ∂Ω and α = λ2 the second eigenvalue of the Laplacian with Dirichlet boundary condition. This extends a result proved in the case of the Euclidean plane by C. Berenstein.  相似文献   

14.
Let
be the Fejér kernel, C be the space of contiuous 2π-periodic functions f with the norm , let
be the Jackson polynomials of the function f, and let
be the Fejér sums of f. The paper presents upper bounds for certain quantities like
which are exact in order for every function f ∈ C. Special attention is paid to the constants occurring in the inequalities obtained. Bibliography: 14 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 90–114.  相似文献   

15.
A solution u of a Cauchy problem for a semilinear heat equation
is said to undergo Type II blowup at t =  T if lim sup Let be the radially symmetric singular steady state. Suppose that is a radially symmetric function such that and (u 0) t change sign at most finitely many times. We determine the exact blowup rate of Type II blowup solution with initial data u 0 in the case of p > p L , where p L is the Lepin exponent.  相似文献   

16.
In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian
((1.λ))
and
((2.λ))
are studied and some new multiplicity results of solutions for systems (1.λ) and (2.λ) are obtained. Moreover, by using the KKM principle we give also two new existence results of solutions for systems (1.1) and (2.1). This Work is supported in part by the National Natural Science Foundation of China (10561011).  相似文献   

17.
In this paper we prove that a function is the continuous value of the Tug-of-War game described in Y. Peres et al. (J. Am. Math. Soc., 2008, to appear) if and only if it is the unique viscosity solution to the infinity Laplacian with mixed boundary conditions
By using the results in Y. Peres et al. (J. Am. Math. Soc., 2008, to appear), it follows that this viscous PDE problem has a unique solution, which is the unique absolutely minimizing Lipschitz extension to the whole (in the sense of Aronsson (Ark. Mat. 6:551–561, 1967) and Y. Peres et al. (J. Am. Math. Soc., 2008, to appear)) of the Lipschitz boundary data . Partially supported by project MTM2004-02223, MEC, Spain, project BSCH-CEAL-UAM and project CCG06-UAM\ESP-0340, CAM, Spain. FC also supported by a FPU grant of MEC, Spain. JDR partially supported by UBA X066 and CONICET, Argentina.  相似文献   

18.
Yong-Zhuo Chen 《Positivity》2008,12(4):643-652
Let A and H be two operators defined in an ordered Banach space such that
, and
, where . This paper discusses the conditions which will guarantee the existence of an asymptotically attractive fixed point for T = A + H.   相似文献   

19.
First of all, by studying the existence and stability of traveling wave fronts of the following nonlinear nonlocal model equation
we derive relation between speed index function and stability index function for each of the waves. This model was derived when studying working memory in synaptically coupled neuronal networks, which incorporates low persistent activity rate θ and high saturating rate Θ. We will investigate dynamics of neuronal waves. For this purpose, we will be concerned with the equation for several different kinds of symmetric and asymmetric kernels and will compare speeds of the waves. Our analysis and results on the speed index functions facilitate our investigation on stability of the waves and the estimates of speeds. Secondly, we are concerned with standing waves of the nonlinear nonhomogeneous system of integral-differential equations
and the scalar equation
Dedicated to Professor Yulin Zhou on the occasion of his eighty-fifth birthday.  相似文献   

20.
For a trigonometric series
defined on [−π, π) m , where V is a certain polyhedron in R m , we prove that
if the coefficients a k satisfy the following Sidon-Telyakovskii-type conditions:
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 579–585, May, 2008.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号