共查询到20条相似文献,搜索用时 15 毫秒
1.
Alois Kastner-Maresch 《Numerical Functional Analysis & Optimization》2013,34(9-10):937-958
This paper is concerned with the application of implicit Runge-Kutta methods suitable for stiff initial value problems to initial value problems for differential inclusions with upper semicontinuous right-hand sides satisfying a uniform one-sided Lipschitz condition and a growth condition. The problems could stem from differential equations with state discontinuous right-hand sides. It is shown that there exist methods with higher order of convergence on intervals where the solution is smooth enough. Globally we get at least the order one. 相似文献
2.
In this article we study the well-posedness of the initial value problem for quasi-linear weakly hyperbolic equations of second order. We obtain a sufficient condition for the Cauchy problem to be locally solvable in the class of smooth function. 相似文献
3.
Li Chen Ling Hsiao Gerald Warnecke 《应用数学学报(英文版)》2007,23(1):9-28
This paper considers a kind of strongly coupled cross diffusion parabolic system,which can be usedas the multi-dimensional Lyumkis energy transport model in semiconductor science.The global existence andlarge time behavior are obtained for smooth solution to the initial boundary value problem.When the initialdata are a small perturbation of an isothermal stationary solution,the smooth solution of the problem under theinsulating boundary condition,converges to that stationary solution exponentially fast as time goes to infinity. 相似文献
4.
M. V. Urev 《Siberian Mathematical Journal》2014,55(3):548-563
We consider an initial boundary value problem for the system of the Maxwell equations in a bounded domain with smooth boundary on a finite time interval with new boundary conditions with memory. In appropriate function spaces, we define and study the nonselfadjoint operator that is generated by the Maxwell operator under a boundary condition with memory. Using the operator method, we prove an existence and uniqueness theorem for a solution to the initial boundary value problem. 相似文献
5.
Jiaqing Pan 《Journal of Mathematical Analysis and Applications》2007,325(1):703-714
In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which depends on initial data in L1 continuously. 相似文献
6.
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
7.
We consider an evolution which starts as a flow of smooth surfaces in nonparametric form propagating in space with normal speed equal to the mean curvature of the current surface. The boundaries of the surfaces are assumed to remain fixed. G. Huisken has shown that if the boundary of the domain over which this flow is considered satisfies the “mean curvature” condition of H. Jenkins and J. Serrin (that is, the boundary of the domain is convex “in the mean”) then the corresponding initial boundary value problem with Dirichlet boundary data and smooth initial data admits a smooth solution for all time. In this paper we consider the case of arbitrary domains with smooth boundaries not necessarily satisfying the condition of Jenkins-Serrin. In this case, even if the flow starts with smooth initial data and homogeneous Dirichlet boundary data, singularities may develop in finite time at the boundary of the domain and the solution will not satisfy the boundary condition. We prove, however, existence of solutions that are smooth inside the domain for all time and become smooth up to the boundary after elapsing of a sufficiently long period of time. From that moment on such solutions assume the boundary values in the classical sense. We also give sufficient conditions that guarantee the existence of classical solutions for all time t ≧ 0. In addition, we establish estimates of the rate at which solutions tend to zero as t → ∞. 相似文献
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This paper concerns an initial–boundary value problem of the inhomogeneous incompressible MHD equations in a smooth bounded domain. The viscosity and resistivity coefficients are density-dependent. The global well-posedness of strong solutions is established, provided the initial norms of velocity and magnetic field are suitably small in some sense, or the lower bound of the transport coefficients are large enough. More importantly, there is not any smallness condition on the density and its gradient. 相似文献
11.
Kiyotsugu Takaba Yutaka Ichihara 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(4):377-396
This paper considers the initial value problem of an interconnection composed of linear systems described by the first-order differential/algebraic equations (DAEs). An initial condition of the system variable for which the DAE has a solution is called admissible. For the interconnected system, we formulate the invariance of the admissible initial condition sets (AICSs) of the sub-systems under interconnection. Namely, the AICSs are said to be invariant if they remain unchanged even when additional constraints due to interconnection are imposed on the system variables. It is shown that the feedback and regular feedback structures of the interconnection guarantee the invariance of the AICSs in the senses of impulsive-smooth distributions and smooth distributions, respectively. The results in this paper justify the use of a feedback controller in the control system design. 相似文献
12.
P. Dutt 《Numerische Mathematik》1999,81(3):323-344
Summary. In this paper we consider hyperbolic initial boundary value problems with nonsmooth data. We show that if we extend the time
domain to minus infinity, replace the initial condition by a growth condition at minus infinity and then solve the problem
using a filtered version of the data by the Galerkin-Collocation method using Laguerre polynomials in time and Legendre polynomials
in space, then we can recover pointwise values with spectral accuracy, provided that the actual solution is piecewise smooth.
For this we have to perform a local smoothing of the computed solution.
Received August 1, 1995 / Revised version received August 19, 1997 相似文献
13.
The authors study the singular diffusion equationwhere Ω(?)Rn is a bounded domain with appropriately smooth boundary δΩ, ρ(x) = dist(x,δΩ), and prove that if α≥p-1, the equation admits a unique solution subject only to a given initial datum without any boundary value condition, while if 0 <α< p - 1, for a given initial datum, the equation admits different solutions for different boundary value conditions. 相似文献
14.
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
15.
Shota Sato 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1383-1392
We consider the Cauchy problem for a parabolic partial differential equation with a power nonlinearity. Our concern in this paper is the existence of a singular solution with smooth initial data. By using the Haraux-Weissler equation, it is shown that there exist singular forward self-similar solutions. Using this result, we also obtain a sufficient condition for the singular solution with general initial data including smooth initial data. 相似文献
16.
Rudong Zheng 《Applicable analysis》2018,97(12):2085-2096
In the paper, by the approximation of smooth solutions and a regularization technique, we show the existence and uniqueness of global weak solutions for a two-component Camassa–Holm system with an arbitrary smooth function provided the initial data satisfy some certain sign condition. 相似文献
17.
CuoBoling HanYongqian LvYongqiang FuYiping 《偏微分方程(英文版)》2005,18(2):121-140
In this paper, we prove that there exists a unique global smooth solution for the homogeneous Neumann boundary value problem of the Landau-Lifschitz equation if the initial function is smooth. 相似文献
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《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):303-330
In this paper we show that the solution of an anticipating stochastic differential equation with smooth coefficients and with a random and smooth initial condition possesses an infinitely differentiable density under some non-degeneracy conditions 相似文献
20.
E. V. Chizhonkov 《Computational Mathematics and Mathematical Physics》2011,51(3):423-434
A new approach is proposed for constructing and analyzing piecewise smooth exact solutions of the system of quasilinear hyperbolic
equations that models the simplest electron oscillations in a plasma slab. A necessary and sufficient condition for their
existence and uniqueness is established. An approximate numerical-analytical solution method is constructed for smooth initial
data. 相似文献