共查询到20条相似文献,搜索用时 31 毫秒
1.
D. O. Tsvetkov 《Russian Mathematics (Iz VUZ)》2018,62(12):59-73
We study the problem on small motions of ideal stratified fluid with a free surface, partially covered by crumbling ice. By the method of orthogonal projecting the boundary conditions on the moving surface and, with the help of investigation of some auxiliary problems, the original initial-boundary value problem is reduced to the equivalent Cauchy problem for a second order differential equation in a Hilbert space. We find sufficient existence conditions for existence of a strong (with respect to the time variable) solution to the initial-boundary value problem describing evolution of the specified hydrodynamics system. 相似文献
2.
A. A. Amosov 《Journal of Mathematical Sciences》2010,165(1):1-41
We consider a nonstationary nonlinear initial-boundary value problem governing radiative-conductive heat transfer in a periodic
system of grey heat shields. The existence and uniqueness of a weak solution and a regular weak solution are established.
Estimates for the solutions in terms of the data of the problem are obtained. Bibliography: 36 titles. 相似文献
3.
The branches of solutions of a nonlinear integral equation of Volterra type in a Banach space are constructed by the successive
approximation method. We consider the case in which a solution may have an algebraic branching point. We reduce the equation
to a system regular in a neighborhood of the branching point. Continuous and generalized solutions are considered. General
existence theorems are used to study an initial-boundary value problem with degeneration in the leading part. 相似文献
4.
This work deals with the study of an initial-boundary value problem in linear theory of thermo-viscoelastic dielectrics. A variational formulation of this problem is provided and the existence of its solution is proved by an auxiliary Faedo-Galerkin scheme. Finally, the uniqueness of the solution is obtained as a corollary of the existence proof. 相似文献
5.
We study the asymptotic behavior as time tends to infinity of the solution of an initial-boundary value problem for a system
of nonlinear integro-differential equations that arises in the mathematical modeling of penetration of electromagnetic field
into a medium whose electric conductivity substantially depends on temperature. Both homogeneous and inhomogeneous boundary
conditions are considered. The exponential stabilization of the solution is established. 相似文献
6.
Global C1 Solution to the Initial-boundary Value Problem for Diagonal Hyperbolic Systems with Linearly Degenerate Characteristics
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We prove that the Cº boundedness of solution implies the global existence and uniqueness of C¹ solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C¹ solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity. 相似文献
7.
We consider an initial-boundary value problem for a one-dimensional parabolic equation with nonlocal boundary conditions. These nonlocal conditions are given in terms of integrals. Based on solution of the Dirichlet problem for the parabolic equation, we constructively establish the well-posedness for the nonlocal problem. 相似文献
8.
Optimal boundary force control at one end of a string for a given displacement mode at the other end
We solve the problem of optimal boundary force control at one end of a string for the case of a given displacement mode at
the other end. The problem is studied in the sense of a generalized solution of the corresponding mixed initial-boundary value
problem in the Sobolev space. We also solve the problem of choosing an optimal boundary control from infinitely many feasible
controls. The generalized solution of the mixed initial-boundary value problem is constructed in closed form, and the uniqueness
of the solution is proved. 相似文献
9.
This paper deals with the Neumann initial-boundary value problem for a classical chemotaxis system with signal consumption in a disk.In contrast to previous studies which have established a comprehensive theory of global classical solutions for suitably regular nonnegative initial data,the focus in the present work is on the question to which extent initially prescribed singularities can be regularized despite the presence of the nonlinear cross-diffusive interaction.The main result in this paper asserts that at least in the framework of radial solutions immediate regularization occurs under an essentially optimal condition on the initial distribution of the population density.More precisely,it will turn out that for any radially symmetric initial data belonging to the space of regular signed Borel measures for the population density and to L2 for the signal density,there exists a classical solution to the Neumann initial-boundary value problem,which is smooth and approaches the given initial data in an appropriate trace sense. 相似文献
10.
A. A. Nikitin 《Differential Equations》2013,49(5):645-653
We prove the uniqueness of a generalized solution of an initial-boundary value problem for the wave equation with boundary conditions of the third and second kind. In addition, we find a closed-form expression for the analytic solution of that problem with zero initial data. The result plays an important role in the investigation of the boundary control problem. We show how to use the obtained solution for the investigation of the boundary control problem in the case of subcritical time intervals for which the solution of the boundary control problem, if it exists at all, is unique. We obtain necessary and sufficient conditions for the existence of a unique solution in a class admitting the existence of finite energy. 相似文献
11.
We prove the existence, uniqueness, and monotonicity of the solution of an upwind conservative explicit difference scheme approximating an initial-boundary value problem for a many-dimensional nonlinear scalar conservation law with a quadratic nonlinearity under some specific conditions imposed only on the input data of the problem. We show that the resulting solution is not necessarily stable. Under some additional conditions on the input data, which provide the absence of shock waves, we prove the stability of the unique solution of the difference scheme for any finite time. 相似文献
12.
In this paper we focus on the initial-boundary value problem of the 2-D isentropic Euler equations with damping. We prove the global-in-time existence of classical solution to the initial-boundary value problem for small smooth initial data by the method of local existence of solution combined with a priori energy estimates, where the appropriate boundary condition plays an important role. 相似文献
13.
The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum
hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a momentum balance
equation equivalent to a compressible Euler equations corrected by a dispersion term of the third order in the momentum balance.
The proof is based on a priori estimates for the energy functional for a new observable constructed with an auxiliary function,
and it is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after
a finite time. 相似文献
14.
We study the large-time behavior of the solution of an initial-boundary value problem for the equations of 1D motions of a compressible viscous heat-conducting gas coupled to radiation through a radiative transfer equation. Assuming suitable hypotheses on the transport coefficients and adapted boundary conditions, we prove that the unique strong solution of this problem converges toward a well-determined equilibrium state at exponential rate. 相似文献
15.
We study the first initial-boundary value problem for the Schrödinger system in a cylindrical domain. It is assumed that the boundary contains a conical point. We obtain an asymptotic expansion of the solution in a neighborhood of such a point. 相似文献
16.
We consider the problem of boundary control by a force applied to one end of a string in the case of a given force mode at
the other end. The problem is studied in the sense of the generalized solution of the corresponding mixed initial-boundary
value problem in the Sobolev space. We also solve the problem of choosing an optimal boundary control in the set of all admissible
controls. The generalized solution of the mixed initial-boundary value problem is constructed in closed form, and its uniqueness
is proved. 相似文献
17.
In our paper we investigated the initial-boundary value problem for elastic layer situated on half space of another elastic medium. In this medium the thermomechanical interactions were taken into consideration. The system of equations with initial-boundary conditions describes the phenomenon of wave propagation with finite speed. In our problem there are two surfaces ie. free surface and contact surface between layer and half space. On the free surface are setting boundary conditions for normal and tangent surface force. We consider two types of contact between layer and half-space: rigid contact and slip contact. The initial-boundary value problem was solved by using integral transformations and Cagniard-de Hoope methods. From the solution of this problem follows that in layer and half space exist some kind of thermoelastic waves. We investigated moreover the conditions which should be fullfiled for propagation of Rayleigh and Love's type waves on the contact surface between layers and half space. The results obtained in our investigation were used in technical applications especially engineering design and diagnostics of roads and airfields. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
A. M. Denisov 《Computational Mathematics and Mathematical Physics》2011,51(9):1588-1595
An initial-boundary value problem for the diffusion equation with an unknown initial condition is considered. Additional information
used for determining the unknown initial condition is an external volume potential whose density is the Laplacian calculated
for the solution of the initial-boundary value problem. Uniqueness theorems for the inverse problem are proved in the case
when the spatial domain of the initial-boundary value problem is a spherical layer or a parallelepiped. 相似文献
19.
A formal asymptotic representation is constructed for the solution of an initial-boundary value problem for a singularly perturbed
system of parabolic equations. A specific feature of the problem is that its solution has an internal transition layer. 相似文献
20.
We numerically analyze the laminar-turbulent transition in the problem on the flow of a viscous incompressible fluid from
a ledge. To model the fluid flow, we use the Boltzmann integro-differential equations expanded in the Knudsen number. For
the fundamental analysis, we use a numerical method of increased accuracy for the integration of the initial-boundary value
problem. By analyzing the phase portraits of the behavior of the system, we find that the transition from a stationary solution
to an irregular chaotic one takes place in accordance with the Feigenbaum-Sharkovskii-Magnitskii scenario. Moreover, the transition
process differs from the results obtained by using the Navier-Stokes equations for solving a similar initial-boundary value
problem. 相似文献