共查询到20条相似文献,搜索用时 31 毫秒
1.
V. M. Luchko 《Journal of Mathematical Sciences》2009,160(3):296-307
We prove the existence and establish some estimates of a solution of the Cauchy problem for a parabolic pulse-action equation
of higher order in t.
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 17–24, January–March, 2008. 相似文献
2.
In a domain with free boundary, we establish conditions for the existence and uniqueness of a solution of the inverse problem
of finding the time-dependent coefficient of heat conductivity. We study the case of strong degeneration where the unknown
coefficient tends to zero as t → +0 as a power function t
β
, where β ≥ 1.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 28–43, January, 2009. 相似文献
3.
V. P. Gaevoi 《Journal of Applied and Industrial Mathematics》2011,5(1):51-64
For a system of first-order partial differential equations describing a catalytic process in a fluidized bed, we consider
a mixed problem in the half-strip 0 ≤ x ≤ h, t ≥ 0. We prove the existence and uniqueness of a bounded summable generalized solution and study its stability. We prove the
stabilization as t → ∞ of the values of some physically meaningful functionals of the solution. 相似文献
4.
We consider a nonlinear pseudoparabolic variational inequality in a tube domain semibounded in variablet. Under certain conditions imposed on coefficients of the inequality, we prove the theorems of existence and uniqueness of
a solution without any restriction on its behavior ast→−∞.
Lvov University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 328–337, March, 1999. 相似文献
5.
A. N. Zarubin 《Ukrainian Mathematical Journal》1997,49(10):1501-1506
By using the method of integral equations, we prove the existence and uniqueness of a regular solution of the Cauchy problem
for a degenerating hyperbolic equation with retarded argument.
Orel Pedagogic Institute, Russia. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 10, pp. 1332–1336, October,
1997. 相似文献
6.
Ya. I. Bigun 《Ukrainian Mathematical Journal》1997,49(5):798-804
For a system of quasilinear hyperbolic equations with a system of differential equations with lag, we prove theorems on the
existence and uniqueness of a solution of the Cauchy problem and its continuous dependence on the initial conditions.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 715–719, May, 1997. 相似文献
7.
In a domain with free boundary, we consider an inverse problem of determining the time-dependent leading coefficient of a
parabolic equation, which tends to zero as t → 0 like a certain given function. Conditions for the existence and uniqueness of a classical solution in the case of weak
degeneration are established. 相似文献
8.
N. V. Artamonov 《Mathematical Notes》2000,67(1):12-19
We study the strong stability of the equation describing small oscillations of an elastic pipe conveying an ideal fluid. We
prove the existence and uniqueness theorem for the generalized solution and find sufficient conditions for strong stability
in the case of a pulsing fluid.
Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 15–24, January, 2000. 相似文献
9.
I. V. Dombrovskii 《Ukrainian Mathematical Journal》1999,51(11):1779-1781
We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu
tt
- uxx = ƒ(x, t, u, u, u
x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ [0, π] ×R, and prove a theorem on the existence and uniqueness of a solution.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1574–1576, November, 1999. 相似文献
10.
Summary. We consider the Cauchy problem for the mass density ρ of particles which diffuse in an incompressible fluid. The dynamical
behaviour of ρ is modeled by a linear, uniformly parabolic differential equation containing a stochastic vector field. This
vector field is interpreted as the velocity field of the fluid in a state of turbulence. Combining a contraction method with
techniques from white noise analysis we prove an existence and uniqueness result for the solution ρ∈C
1,2([0,T]×ℝ
d
,(S)*), which is a generalized random field. For a subclass of Cauchy problems we show that ρ actually is a classical random field,
i.e. ρ(t,x) is an L
2-random variable for all time and space parameters (t,x)∈[0,T]×ℝ
d
.
Received: 27 March 1995 / In revised form: 15 May 1997 相似文献
11.
V. Varlamov 《Mathematical Methods in the Applied Sciences》1996,19(8):639-649
We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for discontinuous initial perturbations this solution is infinitely differentiable with respect to time t and space co-ordinates for t>0 on a bounded time interval. 相似文献
12.
M. L. Gorbachuk 《Ukrainian Mathematical Journal》2000,52(5):680-693
We find conditions on a closed operator A in a Banach space that are necessary and sufficient for the existence of solutions
of a differential equation y′(t) = Ay(t), t ∈[0,∞),in the classes of entire vector functions with given order of growth and type. We present criteria for the denseness
of classes of this sort in the set of all solutions. These criteria enable one to prove the existence of a solution of the
Cauchy problem for the equation under consideration in the class of analytic vector functions and to justify the convergence
of the approximate method of power series. In the special case where A is a differential operator, the problem of applicability
of this method was first formulated by Weierstrass. Conditions under which this method is applicable were found by Kovalevskaya. 相似文献
13.
N. M. Bokalo 《Journal of Mathematical Sciences》1997,85(6):2260-2266
The paper contains theorems on the uniqueness and existence of a generalized solution to the Fourier problem (the problem
without initial conditions) for a class of strongly nonlinear parabolic equations, without any restrictions on the behavior
of the data and of the solution ast → ∞. A priori estimates of the solution are obtained as well. Bibliography: 8 titles.
Dedicated to Olga Arsenievna Oleinik
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000. 相似文献
14.
Zhi-Qiang Shao Ya-Chun Li De-Xing Kong 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(6):935-968
For the Cauchy problem with a kind of non-smooth initial data for weakly linearly degenerate hyperbolic systems of conservation
laws with the linear damping term, we prove the existence and uniqueness of global weakly discontinuous solution u = u(t, x) containing only n weak discontinuities with small amplitude on t ≥ 0, and this solution possesses a global structure similar to that of the similarity solution of the corresponding homogeneous Riemann problem. As an application of our result, we obtain the existence and uniqueness
of global weakly discontinuous solution, continuous and piecewise C
1 solution with discontinuous first order derivatives, of the flow equations of a model class of fluids with viscosity induced
by fading memory.
De-Xing Kong: Supported by the National Science Foundation of China(Grant 10371073), the Special Funds for Major State Basic
Research Projects of China (Grant 2000077306), the Qi Ming Xing programme of Shanghai Government, and the Project sponsored
by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the Ministry of Education of China. 相似文献
15.
N. A. Karazeeva 《Journal of Mathematical Sciences》2000,99(1):870-873
The system of equations describing the 2D flow of a Maxwell fluid is considered. The global existence of a weak solution for
the initial boundary-value problem with periodic boundary conditions is proved. The result allows us to prove the solvability
of the corresponding, Cauchy problem. Bibliography: 9 titles.
Dedicated to the memory of A. P. Oskolkov
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 243, 1997, pp. 111–117.
Translated by N. A. Karazeeva. 相似文献
16.
We consider the general initial-boundary-value problem for a linear parabolic equation of arbitrary even order in anisotropic
Sobolev spaces. We prove the existence and uniqueness of a solution and establish ana priori estimate for it.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1534–1548, November, 1999. 相似文献
17.
We study the problem of existence of periodic and almost periodic solutions of the scalar equation x′ (t) = − δx(t) + pmax
u∈[t − h, t]
x(u) + f(t) where δ, p ∈ R, with a periodic (almost periodic) perturbation f(t). For these solutions, we establish conditions of global exponential stability and prove uniqueness theorems.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 747–754, June, 1998. 相似文献
18.
We introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous definition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness. 相似文献
19.
We prove the existence and uniqueness of the fundamental solution for Kolmogorov operators associated to some stochastic processes, that arise in the Black & Scholes setting for the pricing problem relevant to path dependent options. We improve previous results in that we provide a closed form expression for the solution of the Cauchy problem under weak regularity assumptions on the coefficients of the differential operator. Our method is based on a limiting procedure, whose convergence relies on some barrier arguments and uniform a priori estimates recently discovered. 相似文献
20.
Global existence and asymptotic behavior of solution for Rosenau equation with Stokes damped term 下载免费PDF全文
We study the small‐data Cauchy problem for n‐dimensional Stokes damped Rosenau equation. Under some assumptions, we prove the global existence and uniqueness of the small‐amplitude solution by utilizing the contraction mapping principle and study the asymptotic behavior of the solution. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献