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1.
The steady mixed convection boundary layer flow over a vertical surface with prescribed heat flux is revisited in this Note.
The subset of solutions which can be obtained with the aid of the Reynolds analogy is discussed in a close relationship with the dual solutions reported by Merkin and Mahmood [1] for impermeable, and more
recently by Ishak et al. [2], for permeable surfaces.
相似文献
2.
Zongming Guo 《Applicable analysis》2013,92(1-4):173-189
The existence and uniqueness of positive radial solutions of the equations of the type [IML0001] in BR, p>1 with Dirichlet condition are proved for λ large enough and f satisfying a condition[IML0002] is non-decreasing on [IML0003] It is also proved that all the positive solutions in C1 0(BR) of the above equations are radially symmetric solutions for f satisfying [IML0004] and λ large enough. 相似文献
3.
D. T. Allemang 《International Journal of Game Theory》2002,30(4):539-556
Two approaches have been used to solve impartial games with misère play; genus theory, which has resulted in a number of results summarized in [2], and Sibert-Conway decomposition [9], which has been used to solve the octal game 0.77 (known as Kayles). The main aim of this paper is to publish (for the
first time) the results archived in [1], extending genus theory beyond the applications to which it has previously been applied.
In addition, we extend a result from [6] to misère play by adapting it to use the extended genus theory. The resulting theorems
require extensive calculations to verify that their preconditions hold for any particular games. These calculations have been
carried out by computer for all two-digit octal games. For many of these games, this has resulted in complete solutions. Complete
solutions are presented for four games listed in [8] as unsolved.
Received: September 2001 相似文献
4.
Hermano Frid 《Bulletin of the Brazilian Mathematical Society》2001,32(1):1-35
In this paper we survey recent results on the decay of periodic and almost periodic solutions of conservation laws. We also recall some recent results on the global existence of periodic solutions of conservation laws systems which lie inBV
loc
and are constructed through Glimm scheme. The latter motivates a discussion on a possible strategy for solving the open problem of the global existence of periodic solutions of the Euler equations for nonisentropic gas dynamics. We base our decay analysis on a general result about space-time functions which are almost periodic in the space variable, established here for the first time. This result is an abstract version of Theorem 2.1 in [31], which in turn is an extention of the combined result given by Theorems 3.1–3.2 in [9]. 相似文献
5.
The general γ-attenuation problem is considered for systems with statedependent noise. It is shown that if a controller exists which stabilizes a system with disturbance attenuation then certain LMI's must have positive-definite solutions satisfying a complementary rank condition. If such solutions exist for the considered LMI's the controller is obtained also by solving an LMI. In the absence of the noise the LMI's involved reduce to the ones introduced by Gahinet and al in [7] 相似文献
6.
This paper deals with the use of the Galerkin approximation for calculating branches of steady-state solutions. It is motivated by the analysis of a reaction-diffusion system modeled by a pair of nonlinear partial differential equations on a two-dimensional domain. The goal is to check the possibility of closed loops emerging from a trivial branch. This issue is of importance in recent theories on morphogenesis in embryos (Kauffman et al. [3]). Numerical methods for continuing Galerkin approximations of the steady states give arcs of stable or unstable solutions. The numerical results are in agreement with the predictions of Brezzi et al. [6–8]. In particular, bifurcations from the trivial steady-state or symmetry-breaking bifurcations remain bifurcations for the approximate problem.The whole connected set of solutions thus obtained gives new insight into the behavior of solutions to reaction-diffusion equations and strongly advocates Kauffman's theory. 相似文献
7.
In this paper a linearly perturbed version of the well-known matrix Riccati equations which arise in certain stochastic optimal control problems is studied. Via the
concepts of mean square stabilizability and mean square detectability we improve previous results on both the convergence properties of the linearly perturbed Riccati differential equation and the solutions of the linearly perturbed algebraic Riccati equation. Furthermore, our approach unifies, in some way, the study for this class of Riccati equations with the one for classical
theory, by eliminating a certain inconvenient assumption used in previous works (e.g., [10] and [26]). The results are derived
under relatively weaker assumptions and include, inter alia, the following: (a) An extension of Theorem 4.1 of [26] to handle systems not necessarily observable. (b) The existence of
a strong solution, subject only to the mean square stabilizability assumption. (c) Conditions for the existence and uniqueness of stabilizing
solutions for systems not necessarily detectable. (d) Conditions for the existence and uniqueness of mean square stabilizing
solutions instead of just stabilizing. (e) Relaxing the assumptions for convergence of the solution of the linearly perturbed
Riccati differential equation and deriving new convergence results for systems not necessarily observable.
Accepted 30 July 1996 相似文献
8.
We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical
case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions.
While the only small self-similar solution in the strong
Lp{\cal L}^{p}
space is the null solution, infinitely many self-similar solutions do exist in weak-
Lp{\cal L}^{p}
spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained
in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained. 相似文献
9.
Yanyan Li 《纯数学与应用数学通讯》1996,49(6):541-597
This is a sequel to [30], which studies the prescribing scalar curvature problem on Sn. First we present some existence and compactness results for n = 4. The existence result extends that of Bahri and Coron [4], Benayed, Chen, Chtioui, and Hammami [6], and Zhang [39]. The compactness results are new and optimal. In addition, we give a counting formula of all solutions. This counting formula, together with the compactness results, completely describes when and where blowups occur. It follows from our results that solutions to the problem may have multiple blowup points. This phenomena is new and very different from the lower-dimensional cases n = 2, 3. Next we study the problem for n ≥ 3. Some existence and compactness results have been given in [30] when the order of flatness at critical points of the prescribed scalar curvature functions K(x) is β ϵ (n − 2, n). The key point there is that for the class of K mentioned above we have completed L∞ apriori estimates for solutions of the prescribing scalar curvature problem. Here we demonstrate that when the order of flatness at critical points of K(x) is β = n − 2, the L∞ estimates for solutions fail in general. In fact, two or more blowup points occur. On the other hand, we provide some existence and compactness results when the order of flatness at critical points of K(x) is β ϵ [n − 2,n). With this result, we can easily deduce that C∞ scalar curvature functions are dense in C1,α (0 < α < 1) norm among positive functions, although this is generally not true in the C2 norm. We also give a simpler proof to a Sobolev-Aubin-type inequality established in [16]. Some of the results in this paper as well as that of [30] have been announced in [29]. © 1996 John Wiley & Sons, Inc. 相似文献
10.
Mikhail Kovalyov 《纯数学与应用数学通讯》1987,40(5):589-607
In this paper we consider the initial value problem for the nonlinear wave equation □u = F(u, u′) in Friedman-Robertson-Walker space-time, □ being the D'Alambertian in local coordinates of space-time. We obtain decay estimates and show that the equation has global solutions for small initial data. We do it by reducing the problem to an initial value problem for the wave equation over hyperbolic space. As byproduct we derive decay and global existence for solutions of the wave equation over the hyperbolic space with small initial data. The same technique with some auxiliary lemmas similar to the ones proved in [6], [7] can be used to generalize the result to the case when F depends also on second derivatives of u in a certain way. 相似文献
11.
Gonzalo Contreras 《Calculus of Variations and Partial Differential Equations》2001,13(4):427-458
For convex superlinear lagrangians on a compact manifold M we characterize the Peierls barrier and the weak KAM solutions of the Hamilton-Jacobi equation, as defined by A. Fathi [9],
in terms of their values at each static class and the action potential defined by R. Ma né [14]. When the manifold M is non-compact, we construct weak KAM solutions similarly to Busemann functions in riemannian geometry. We construct a compactification
of by extending the Aubry set using these Busemann weak KAM solutions and characterize the set of weak KAM solutions using this
extended Aubry set.
Received: 13 November 2000 / Accepted: 4 December 2000 / Published online: 25 June 2001 相似文献
12.
Penalty methods form a well known technique to embed elliptic variational inequality problems into a family of variational equations (cf. [6], [13], [17]). Using the specific inverse monotonicity properties of these problems L ∞-bounds for the convergence can be derived by means of comparison solutions. Lagrange duality is applied to estimate parameters involved. For piecewise linear finite elements applied on weakly acute triangulations in combination with mass lumping the inverse monotonicity of the obstacle problems can be transferred to its discretization. This forms the base of similar error estimations in the maximum norm for the penalty method applied to the discrete problem. The technique of comparison solutions combined with the uniform boundedness of the Lagrange multipliers leads to decoupled convergence estimations with respect to the discretization and penalization parameters. 相似文献
13.
This paper presents complete solutions of the stationary distributions of buffer occupancy and buffer content of a fluid queue driven by an M/M/1 queue. We assume a general boundary condition when compared to the model discussed in Virtamo and Norros [Queueing Systems 16 (1994) 373–386] and Adan and Resing [Queueing Systems 22 (1996) 171–174]. We achieve the required solutions by transforming the underlying system of differential equations using Laplace transforms to a system of difference equations leading to a continued fraction. This continued fraction helps us to find complete solutions. We also obtain the buffer content distribution for this fluid model using the method of Sericola and Tuffin [Queueing Systems 31 (1999) 253–264]. 相似文献
14.
We prove the weighted Strichartz estimates for the wave equation in even space dimensions with radial symmetry in space. Although the odd space dimensional cases have been treated in our previous paper [5], the lack of the Huygens principle prevents us from a similar treatment in even space dimensions. The proof is based on the two explicit representations of solutions due to Rammaha [11] and Takamura [14] and to Kubo-Kubota [6]. As in the odd space dimensional cases [5], we are also able to construct self-similar solutions to semilinear wave equations on the basis of the weighted Strichartz estimates.Mathematics Subject Classification (2000): 35L05, 35B45, 35L70COE fellowDedicated to Professor Mitsuru Ikawa on the occasion of his sixtieth birthday 相似文献
15.
Krzysztof Chemiski 《Mathematical Methods in the Applied Sciences》1998,21(1):43-58
This paper is a continuation of the work [9]. We prove the uniqueness result for global in time large solutions of dynamic equations to an inelastic model of material behaviour of metals in the two-dimensional case, provided a higher regularity of the solutions. Moreover, the 𝕃p-stability for p<2 of the solutions in the case of homogeneous boundary data is established. © 1998 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
16.
Gabriel Koch Nikolai Nadirashvili Gregory A. Seregin Vladimir Šverák 《Acta Mathematica》2009,203(1):83-105
We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in R
n
× (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of
existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to
some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent
paper by Chen, Strain, Tsai and Yau [4]. 相似文献
17.
I. W. Rodrigues 《Applicable analysis》2013,92(1-4):45-55
Let a, c [euro] (0, ∞), b [euro] [IML0001] and let k be a nonnegative integer. We obtain necessary and sufficient conditions for all positive solutions of the nonlinear difference equation [IML0002] to oscillate about its positive equilibrium. When k = 0, we obtain necessary and sufficient conditions for the positive equilibrium of Eq. (?) to be a global attractor of all positive solutions. 相似文献
18.
Peter Benner Ren-Cang Li Ninoslav Truhar 《Journal of Computational and Applied Mathematics》2009,233(4):1035-1045
This paper is concerned with the numerical solution of large scale Sylvester equations AX−XB=C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) [22] and Li and White (2002) [20] demonstrated that the so-called Cholesky factor ADI method with decent shift parameters can be very effective. In this paper we present a generalization of the Cholesky factor ADI method for Sylvester equations. An easily implementable extension of Penz’s shift strategy for the Lyapunov equation is presented for the current case. It is demonstrated that Galerkin projection via ADI subspaces often produces much more accurate solutions than ADI solutions. 相似文献
19.
We study the large-time asymptotics for solutions u( x , t) of the wave equation with Dirichlet boundary data, generated by a time-harmonic force distribution of frequency ω, in a class of domains with non-compact boundaries and show that the results obtained in [11] for a special class of local perturbations of Ω0 ? ?2 × (0,1) can be extended to arbitrary smooth local perturbations Ω of Ω0. In particular, we prove that u is bounded as t → ∞ if Ω does not allow admissible standing waves of frequency ω in the sense of [8]. This implies in connection with [8]. Theorem 3.1 that the logarithmic resonances of the unperturbed domain Ω0 at the frequencies ω = πk (k = 1, 2,…) observed in [14] can be simultaneously removed by small perturbations of the boundary. As a main step of our analysis, the determination of admissible solutions of the boundary value problem ΔU + κ2U = ? f in Ω, U = 0 on ?Ω is reduced to a compact operator equation. 相似文献
20.
This paper deals with the solutions defined for all time of the KPP equation ut = uxx + f(u), 0 < u(x,t) < 1, (x,t) ∈ ℝ2, where ƒ is a KPP‐type nonlinearity defined in [0,1]: ƒ(0) = ƒ(1) = 0, ƒ′(0) > 0, ƒ′(1) < 0, ƒ > 0 in (0,1), and ƒ′(s) ≤ ƒ′(0) in [0,1]. This equation admits infinitely many traveling‐wave‐type solutions, increasing or decreasing in x. It also admits solutions that depend only on t. In this paper, we build four other manifolds of solutions: One is 5‐dimensional, one is 4‐dimensional, and two are 3‐dimensional. Some of these new solutions are obtained by considering two traveling waves that come from both sides of the real axis and mix. Furthermore, the traveling‐wave solutions are on the boundary of these four manifolds. © 1999 John Wiley & Sons, Inc. 相似文献