共查询到20条相似文献,搜索用时 15 毫秒
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《Nonlinear Analysis: Theory, Methods & Applications》2004,57(2):183-189
We study the existence of mild solutions for the nonlocal Cauchy problemand give new criterions, which extend some existing results in this area. 相似文献
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We improve several results published from 1950 up to 1982 on matrix functions commuting with their derivative, and establish two results of general interest. The first one gives a condition for a finite-dimensional vector subspace E(t) of a normed space not to depend on t, when t varies in a normed space. The second one asserts that if A is a matrix function, defined on a set ?, of the form A(t)= U diag(B1(t),…,Bp(t)) U-1, t ∈ ?, and if each matrix function Bk has the polynomial form then A itself has the polynomial form , where , dk being the degree of the minimal polynomial of the matrix Ck, for every k ∈ {1,…,p}. 相似文献
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David W. Bange 《Journal of Differential Equations》1975,17(1):61-72
This paper treats the quasilinear, parabolic boundary value problem u(0, t) = ?1(t); u(l, t) = ?2(t) on an infinite strip with the functions being periodic in t. The major theorem of the paper gives sufficient conditions on for this problem to have a periodic solution u(x, t) which may be constructed by successive approximations with an integral operator. Some corollaries to this theorem offer more explicit conditions on and indicate a method for determining the initial estimate at which the iteration may begin. 相似文献
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F.J. Massey 《Journal of Differential Equations》1976,22(2):416-427
Analyticity in t of solutions u(t) of nonlinear evolution equations of the form , is established under suitable conditions on . An application is given to quasilinear parabolic equations. 相似文献
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Thomas G. Kurtz 《Stochastic Processes and their Applications》1978,6(3):223-240
A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form where , the Y1 are independent Poisson processes, and N is a parameter with a natural interpretation (e.g. total population size or volume of a reacting solution).The corresponding deterministic model, satisfies Under very general conditions limN→∞XN(t)=X(t) a.s. The process XN(t) is compared to the diffusion processes given by and Under conditions satisfied by most of the applied probability models, it is shown that XN,ZN and V can be constructed on the same sample space in such a way that and 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2003,54(1):9-37
In this paper, we study the problemin the setting of the weighted sobolev space . The main novelty of our work is L∞ estimates on the solutions, and the existence of a weak and renormalized solution. 相似文献
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The main result is the following. Let be a bounded Lipschitz domain in , d?2. Then for every with ∫f=0, there exists a solution of the equation divu=f in , satisfying in addition u=0 on and the estimate where C depends only on . However one cannot choose u depending linearly on f. To cite this article: J. Bourgain, H. Brezis, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 973–976. 相似文献
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According to a result of A. Ghizzetti, for any solution y(t) of the differential equation where , (0 ?i ? n ?1, either y(t) = 0 for t ? 1 or there is an integer r with 0 ? r ? n ? 1 such that exists and ≠0. Related results are obtained for difference and differential inequalities. A special case of the former has interesting applications in the study of orthogonal polynomials. 相似文献
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We study the Schrödinger equation iy′+Δy+qy=0 on with Dirichlet boundary data and initial condition and we consider the inverse problem of determining the potential q(x), when is given, where Γ0 is an open subset of satisfying an appropriate geometrical condition. The detailed proof will be given in [1]. To cite this article: L. Baudouin, J.-P. Puel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 967–972. 相似文献
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Charles S Kahane 《Journal of Differential Equations》1979,32(3):454-471
In this paper we study the asymptotic behavior of solutions to the mixed initial boundary value problem for the system of nonlinear parabolic equations We show, under suitable technical assumptions, that these solutions converge to solutions of the Dirichlet problem for the corresponding limiting elliptic system, provided that the solution of the Dirichlet problem is unique. 相似文献
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Min Ming Tang 《Journal of Mathematical Analysis and Applications》1977,57(2):368-381
In this paper we study the behavior of solutions of some quasilinear parabolic equations of the form as t → ∞. In particular, the solutions of these equations will decay to zero as t → ∞ in the L∞ norm. 相似文献
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We construct two d-dimensional independent diffusions , with the same viscosity ν≠0 and the same drift u(x,t)=(pρta(x)v1+(1?p)ρtb(x)v2)/(pρta(x)+(1?p)ρtb(x)), where ρta,ρtb are respectively the density of Xta and Xtb. Here and p∈(0,1) are given. We show that is the unique weak solution of the following pressureless gas system such that as t→0+. To cite this article: A. Dermoune, S. Filali, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
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This paper deals with asymptotic behavior for (weak) solutions of the equation , on + × Ω; u(t, x) = 0, on + × ?Ω. If and β is coercive, we prove that the solutions are bounded in the energy space, under weaker assumptions than those used by G. Prouse in a previous work. If in addition and ? is srongly almost-periodic, we prove for strongly monotone β that all solutions are asymptotically almost-periodic in the energy space. The assumptions made on β are much less restrictive than those made by G. Prouse: mainly, we allow β to be multivalued, and in the one-dimensional case β need not be defined everywhere. 相似文献