共查询到20条相似文献,搜索用时 0 毫秒
1.
Rico Zacher 《Journal of Mathematical Analysis and Applications》2008,348(1):137-149
We investigate linear and quasilinear evolutionary partial integro-differential equations of second order which include time fractional evolution equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these problems. We also show that a maximum principle holds for such equations. 相似文献
2.
D. V. Portnyahin 《Ukrainian Mathematical Journal》2009,61(3):478-489
We study the problem of boundedness of weak solutions of a general nondiagonal parabolic system of nonlinear differential
equations whose matrix of coefficients satisfies special structural conditions. To do this, we use a procedure based on the
estimation of a certain function of unknowns. 相似文献
3.
Joel E. Restrepo Durvudkhan Suragan 《Mathematical Methods in the Applied Sciences》2020,43(15):9080-9089
We give necessary conditions to get oscillatory solutions of a class of fractional order neutral differential equations with continuously distributed delay by means of the fractional derivative with respect to a given function. In particular, oscillatory solutions of the considered fractional equations with Caputo and Hadamard type of fractional derivatives are established. Some explicit examples are given to illustrate the main results. 相似文献
4.
R. S. Makin 《Mathematical Notes》2011,90(1-2):102-124
We consider the system of equations describing transport processes in inhomogeneous distributed media, such as those in nuclear reactors. For a given system of equations, a mixed problem is posed. Under certain conditions on the initial data, we prove the global solvability of the problem in the weak generalized sense by using the standard scheme of nonlinear functional analysis. 相似文献
5.
V. S. Sergeev 《Differential Equations》2017,53(9):1197-1206
We consider equations with nonlinear terms representable by power series in the variable and functionals in integral form. The equation depends on a small exponentially limitperiodic perturbation, i.e., on a function that exponentially tends to a periodic function as the independent variable increases. In the Lyapunov critical case of one zero root, we prove the existence of a family of exponentially limit-periodic solutions of the equation in the form of power series in the small parameter and arbitrary initial values of the noncritical variables. 相似文献
6.
D. V. Portnyagin 《Differential Equations》2008,44(8):1178-1182
By using a method of deriving estimates for linear combinations of solution components, we prove the boundedness of weak solutions of nondiagonal quasilinear parabolic systems whose coefficient matrix satisfies special structural conditions. 相似文献
7.
D. V. Portnyagin 《Ukrainian Mathematical Journal》2006,58(8):1223-1237
The L
∞-estimates of weak solutions are established for a quasilinear nondiagonal parabolic system of singular equations whose matrix
of coefficients satisfies special structural conditions. A procedure based on the estimation of linear combinations of the
unknowns is used.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1084–1096, August, 2006. 相似文献
8.
M. S. Sgibnev 《Differential Equations》2008,44(7):923-934
We obtain an asymptotic expansion of the solution of a system of first-order integro-differential equations with the influence of the roots of the characteristic equation taken into account. A similar expansion is established for a system of Volterra integral equations. 相似文献
9.
10.
11.
Summary In this paper a number of known results on the boundedness of solutions and the existence of periodic solutions of the scalar
equation 1.1(2) are extended to the vector equation 1.1(1). 相似文献
12.
In this paper, we are concerned with the boundedness of all the solutions and the existence of quasiperiodic solutions for some Duffing equations , where e(t) is of period 1, and g : R → R possesses the characters: g(x) is superlinear when x ? d0, d0 is a positive constant and g(x) is semilinear when x ? 0. 相似文献
13.
Jito Vanualailai Shin-ichi Nakagiri 《Journal of Mathematical Analysis and Applications》2003,281(2):602-619
Using new and known forms of Lyapunov functionals, this paper proposes new stability criteria for a system of Volterra integro-differential equations. 相似文献
14.
G. V. Zavizion 《Ukrainian Mathematical Journal》1997,49(12):1819-1826
An asymptotic solution of a system of inegro-differential equations is constructed for the case where turning points are present.
Vinnychenko Kirovograd Pedagogic Institute, Kirovograd. Translated from Ukrainskii Matematicheskii Zhurnal. Vol. 49, No. 12,
pp. 1617–1623, December, 1997 相似文献
15.
Hans Grabmüller 《Integral Equations and Operator Theory》1978,1(1):28-56
Given the linear integro-differential equation (Po) on a reflexive Banach space, we prove the existence of unbounded solutions with an exponential growth rate for a class of initial-value problems. Since the appearing kernel functions are of convolution type on a semi-axis, abstract Wiener-Hopf techniques, recently developed by Feldman [3,4,5], are used for the construction of the resolving operator associated with the problems under consideration. Applicability of the results is shown to initial boundary-value problems arising in the theory of generalized heat conduction in materials with memory and of viscoelasticity. 相似文献
16.
17.
Guy Barles Emmanuel Chasseigne Adina Ciomaga Cyril Imbert 《Journal of Differential Equations》2012,252(11):6012-6060
We establish new Hölder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii–Lions?s method. We thus extend the Hölder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local–nonlocal interaction, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one. 相似文献
18.
John T. Edwards Neville J. Ford 《Journal of Computational and Applied Mathematics》2002,140(1-2):275-289
This paper is concerned with the qualitative behaviour of solutions to difference equations. We focus on boundedness and stability of solutions and we present a unified theory that applies both to autonomous and nonautonomous equations and to nonlinear equations as well as linear equations. Our presentation brings together new, established, and hard-to-find results from the literature and provides a theory that is both memorable and easy to apply. We show how the theoretical results given here relate to some of those in the established literature and by means of simple examples we indicate how the use of Lipschitz constants in this way can provide useful insights into the qualitative behaviour of solutions to some nonlinear problems including those arising in numerical analysis. 相似文献
19.
Summary. Scalar hyperbolic integro-differential equations arise as models for e.g. radiating or self-gravitating fluid flow. We present finite volume schemes on unstructured grids applied to the Cauchy problem for such equations. For a rather general class of integral operators we show convergence of the approximate solutions to a possibly discontinuous entropy solution of the problem. For a specific model problem in radiative hydrodynamics we introduce a convergent fully discrete finite volume scheme. Under the assumption of sufficiently fast spatial decay of the entropy solution we can even establish the convergence rate h1/4|ln(h)| where h denotes the grid parameter. The convergence proofs rely on appropriate variants of the classical Kruzhkov method for local balance laws together with a truncation technique to cope with the nonlocal character of the integral operator.Mathematics Subject Classification (2000): 35L65, 35Q35, 65M15 相似文献