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1.
§1 IntroductionHadamard type well-posedness and Tikhonov type well-posedness are two main typesof concepts of well-posedness. At the beginning of last century,Hadamard firstintroduced the concept of well-posedness in study of optimal problem. Hadamard typewell-posedness of a problem means the continuous dependence of the solution on the dataof such problem. Later,Tikhonov introduced another concept of well-posedness.Tikhonov type well-posedness deals with the behavior ofa prescribed class …  相似文献   

2.
In this paper we show the well-posedness and stability of the Maxwell scattering problem with the transparent boundary condition. The proof depends on the well-posedness of the time-harmonic Maxwell scattering problem with complex wave numbers which is also established.  相似文献   

3.
The local well-posedness of the Cauchy problem for the Hirota equation is established for low regularity data in Sobolev spaces Hs(s≥-1/4). Moreover, the global well-posedness for L2 data follows from the local well-posedness and the conserved quantity. For data in Hs(s > 0), the global well-posedness is also proved. The main idea is to use the generalized trilinear estimates, associated with the Fourier restriction norm method.  相似文献   

4.
We study global well-posedness below the energy norm of the Cauchyproblem for the Klein-Gordon equation in R^n with n≥3. By means of Bourgain‘s method along with the endpoint Strichartz estimates of Keel and Tao, we prove the H^s-global well-posedness with s<1 of the Cauchy problem for the Klein-Gordon equation. This we do by establishing a series of nonlinear a priori estimates in the setting of Besov spaces.  相似文献   

5.
In this article, we study the Cauchy problem to the micropolar Rayleigh–Bénard convection problem without velocity dissipation in two dimension. We first prove the local well-posedness of a smooth solution, and then establish a blow up criterion in terms of the gradient of scalar temperature field. At last, we obtain the global well-posedness to the system.  相似文献   

6.
In this paper, we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic microbeam system, where the heat conduction is given by Gurtin-Pipkin thermal law. We first establish the well-posedness of the system by using the semigroup arguments and Lumer-Phillips theorem. We then obtain an explicit and general formula for the energy decay rates through perturbed energy method and some properties of the convex functions.  相似文献   

7.
The local well-posedness of the Cauchy problem for the fifth order shallow water equation δtu+αδx^5u+βδx^3u+rδxu+μuδru=0,x,t∈R, is established for low regularity data in Sobolev spaces H^s(s≥-3/8) by the Fourier restriction norm method. Moreover, the global well-posedness for L^2 data follows from the local well-posedness and the conserved quantity. For data in H^s(s〉0), the global well-posedness is also proved, where the main idea is to use the generalized bilinear estimates associated with the Fourier restriction norm method to prove that the existence time of the solution only depends on the L^2 norm of initial data.  相似文献   

8.
Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, we prove the propagation of the regularity in the Sobolev spaces HS(IR^2) with s 〉 1. Finally, an ill-posedness result is obtained in HS(IR^2) for s 〈 1.  相似文献   

9.
The well-posedness of the dynamic framework in earth-system model(ESM for short) is a common issue in earth sciences and mathematics.In this paper,the authors first introduce the research history and fundamental roles of the well-posedness of the dynamic framework in the ESM,emphasizing the three core components of ESM,i.e.,the atmospheric general circulation model(AGCM for short),land-surface model(LSM for short) and oceanic general circulation model(OGCM for short) and their couplings.Then,som...  相似文献   

10.
A non-local abstract Cauchy problem with a singular integral is studied, which is a closed system of two evolution equations for a real-valued function and a function-valued function. By proposing an appropriate Banach space, the well-posedness of the evolution system is proved under some boundedness and smoothness conditions on the coefficient functions. Furthermore, an isomorphism is established to extend the result to a partial integro-differential equation with a singular convolution kernel, which is a generalized form of the stationary Wigner equation. Our investigation considerably improves the understanding of the open problem concerning the well-posedness of the stationary Wigner equation with in ow boundary conditions.  相似文献   

11.
We give a unified approach to Hadamard well-posedness for some nonlinear problems such as those of Ky Fan’s point and quasi-variational inequality. As applications, we obtain some well-posed theorems for Nash equilibrium points.  相似文献   

12.
Different notions of well-setness and well-posedness of optimization problems are considered. Connections among these notions are studied. These notions are compared with Hadamard well-posedness.  相似文献   

13.
Cooperation structures without any a priori assumptions on the combinatorial structure of feasible coalitions are studied and a general theory for marginal values, cores and convexity is established. The theory is based on the notion of a Monge extension of a general characteristic function, which is equivalent to the Lovász extension in the special situation of a classical cooperative game. It is shown that convexity of a cooperation structure is tantamount to the equality of the associated core and Weber set. Extending Myerson’s graph model for game theoretic communication, general communication structures are introduced and it is shown that a notion of supermodularity exists for this class that characterizes convexity and properly extends Shapley’s convexity model for classical cooperative games.  相似文献   

14.
Some distinguished types of voters, as vetoes, passers or nulls, as well as some others, play a significant role in voting systems because they are either the most powerful or the least powerful voters in the game independently of the measure used to evaluate power. In this paper we are concerned with the design of voting systems with at least one type of these extreme voters and with few types of equivalent voters. With this purpose in mind we enumerate these special classes of games and find out that its number always follows a Fibonacci sequence with smooth polynomial variations. As a consequence we find several families of games with the same asymptotic exponential behavior except for a multiplicative factor which is the golden number or its square. From a more general point of view, our studies are related with the design of voting structures with a predetermined importance ranking.  相似文献   

15.
In this paper, we investigate the well-posedness of an initial-boundary value problem for the equations of multidimensional radiation hydrodynamics which are a hyperbolic-Boltzmann coupled system. We obtain the local existence and uniqueness of smooth solutions to this problem by using the energy method.  相似文献   

16.
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge–Bäcklund transformation, underlying symmetries among superficially different forms of the equations.  相似文献   

17.
The symmetric coalitional binomial semivalues extend the notion of binomial semivalue to games with a coalition structure, in such a way that they generalize the symmetric coalitional Banzhaf value. By considering the property of balanced contributions within unions, two axiomatic characterizations for each one of these values are provided.  相似文献   

18.
Different (proper as well as improper) simple games may share any nonseparating blocking family. An interesting question is whether all such proper games on one hand, and all improper ones on the other, are isomorphic. The answer is given here and the automorphisms of the blocking family help us to understand the structure and links of all such games.  相似文献   

19.
In this paper we consider symmetric bimatrix games [AAT]. We use a matrix operator s(A), defined as the sum of the cofactors of the given matrix A, for finding the population equilibrium and its fitness in evolutionarily matrix games with all supported strategies, and to complete Bishop-Cannings Theorem.  相似文献   

20.
We introduce and analyze a liar game in which t-ary questions are asked and the responder may lie at most k times. As an additional constraint, there is an arbitrary but prescribed list (the channel) of permissible types of lies. For any fixed t, k, and channel, we determine the exact asymptotics of the solution when the number of queries goes to infinity.  相似文献   

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