共查询到20条相似文献,搜索用时 0 毫秒
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T. E. Moiseev 《Differential Equations》2008,44(5):734-736
We study the solvability of the mixed boundary value problem for the Laplace equation with three distinct boundary conditions, two of which include two directional derivatives with distinct tilt angles and the remaining one is the first boundary condition. An example of a nontrivial solution of the homogeneous problem is given, and conditions under which the problem has a unique solution are established. The solvability of the problem with a nonhomogeneous first boundary condition is studied. 相似文献
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D. V. Churbanov A. Yu. Shcheglov 《Moscow University Computational Mathematics and Cybernetics》2012,36(1):50-52
The inverse problem of reconstructing the right-hand sides of an elliptic equation in a circular domain is studied. The right-hand
sides describe point sources. Under certain conditions, numerical experiments reveal there is a second solution. The results
from experiments are illustrated by figures reflecting the juxtaposition of the two solutions. 相似文献
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王祥 《纯粹数学与应用数学》2015,(2):171-181
研究了一类高阶变形的Novikov方程全局弱解的存在性,在初值满足条件u0∈H2,p,p 4时,通过黏性逼近的方法得到了高阶变形Novikov方程全局弱解的存在性. 相似文献
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A. M. Denisov 《Computational Mathematics and Mathematical Physics》2016,56(10):1737-1742
An initial–boundary value problem for the two-dimensional heat equation with a source is considered. The source is the sum of two unknown functions of spatial variables multiplied by exponentially decaying functions of time. The inverse problem is stated of determining two unknown functions of spatial variables from additional information on the solution of the initial–boundary value problem, which is a function of time and one of the spatial variables. It is shown that, in the general case, this inverse problem has an infinite set of solutions. It is proved that the solution of the inverse problem is unique in the class of sufficiently smooth compactly supported functions such that the supports of the unknown functions do not intersect. This result is extended to the case of a source involving an arbitrary finite number of unknown functions of spatial variables multiplied by exponentially decaying functions of time. 相似文献
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This work investigates the spherical symmetric solutions of more realistic equation of states. We generalize the method of Hsu et al. (Methods Appl. Anal. 8 (2001) 159) to show the existence of spherical symmetric weak solution of the relativistic Euler equation with initial data containing the vacuum state. 相似文献
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Blowups of vorticity for the three- and two-dimensional homogeneous Euler equations are studied. Two regimes of approaching a blow-up point, respectively, with variable or fixed time are analyzed. It is shown that in the n-dimensional ( ) generic case the blowups of degrees at the variable time regime and of degrees at the fixed time regime may exist. Particular situations when the vorticity blows while the direction of the vorticity vector is concentrated in one or two directions are realizable. 相似文献
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We investigate the problem to define statistical solutions for the two-dimensional, periodic Euler Equation and prove a theorem of global existence and uniqueness for a regularized version. Moreover, we deduce the existence of the Euler flow in a weak form. 相似文献
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T. E. Moiseev 《Differential Equations》2014,50(10):1378-1383
We obtain an integral representation of the solution of the Tricomi problem for the Lavrent’ev-Bitsadze equation with mixed boundary conditions in the elliptic part of the domain and with zero posed on one characteristic of the equation. The gradient of the solution is not continuous but satisfies some condition referred to as the “generalized Frankl matching condition.” We state theorems implying that the inhomogeneous Tricomi problem either has a unique solution or is determined modulo a solution of the homogeneous Tricomi problem. 相似文献
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We consider the 3D Navier–Stokes equation with generalized impermeability boundary conditions. As auxiliary results, we prove the local in time existence of a strong solution (‘strong’ in a limited sense) and a theorem on structure. Then, taking advantage of the boundary conditions, we formulate sufficient conditions for regularity up to the boundary of a weak solution by means of requirements on one of the eigenvalues of the rate of deformation tensor. Finally, we apply these general results to the case of an axially symmetric flow with zero angular velocity. 相似文献
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主要研究了一个修正的Novikov方程,并给出了当初值u0(x)满足一定条件时,方程弱解的全局存在性,推广了Novikov方程的相关结果. 相似文献
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B. P. Belinskii 《Journal of Mathematical Sciences》1985,30(5):2378-2385
One establishes uniqueness theorems and one gives examples of nonuniqueness for a series of boundary-contact acoustics problems, i.e. diffraction problems under boundary conditions, described by a higher order operator and vanishing at isolated points.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 128, pp. 21–32, 1983. 相似文献
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A. I. Noarov 《Siberian Mathematical Journal》2012,53(6):1115-1118
We examine the functional-differential equation Δu(x) — div(u(H(x))f (x)) = 0 on a torus which is a generalization of the stationary Fokker-Planck equation. Under sufficiently general assumptions on the vector field f and the map H, we prove the existence of a nontrivial solution. In some cases the subspace of solutions is established to be multidimensional. 相似文献
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We obtain the existence of global‐in‐time weak solutions to the Cauchy problem for a one‐dimensional shallow‐water equation that is formally integrable and can be obtained by approximating directly the Hamiltonian for Euler's equation in the shallow‐water regime. The solution is obtained as a limit of viscous approximation. The key elements in our analysis are some new a priori one‐sided supernorm and space‐time higher‐norm estimates on the first‐order derivatives. © 2000 John Wiley & Sons, Inc. 相似文献
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Dongho Chae 《Journal of Differential Equations》2006,227(2):640-651
We obtain new continuation principle of the local classical solutions of the 3D Euler equations, where the regularity condition of the direction field of the vorticiy and the integrability condition of the magnitude of the vorticity are incorporated simultaneously. The regularity of the vorticity direction field is most appropriately measured by the Triebel-Lizorkin type of norm. Similar result is also obtained for the inviscid 2D quasi-geostrophic equation. 相似文献
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We give an example of non trivial solution of the homogeneous Cauchy problem of the heat equation, which is, for each t, bounded in the space variables. 相似文献