共查询到20条相似文献,搜索用时 46 毫秒
1.
G. Martelli 《Journal of Difference Equations and Applications》2013,19(3):327-331
The explicit solution of four-point linear partial difference equations, provided with variable coefficients and with boundary conditions including the independent variables, was found in a previous note. In addition, the note explained the procedure to be used in case of boundary conditions also including the dependent variables. The aim of this note is to determine the explicit solution of a three-point equation of the above-mentioned second type, encountered in the study of differential difference equations with the method of the steps. 相似文献
2.
Reinhard Farwig 《Acta Appl Math》1994,37(1-2):41-51
In this note, we discuss the reflection principle of the Stokes system in a half space for the threedimensional case, and of the biharmonic equation. Admitting different boundary conditions, we use the reflection principle to prove uniqueness of solutions of the Stokes system or the biharmonic equation in weightedLq-spaces 相似文献
3.
Cheikh Ould Mohamed El-Hafedh Elbar Ould Ely Telmoudy Mohamed Vall Ould Moustapha 《Comptes Rendus Mathematique》2013,351(19-20):747-752
In this note, we give the solutions of the Cauchy problems for the Euler–Poisson–Darboux equations (EPD) with modified conditions in the hyperbolic space with application to the wave equation. 相似文献
4.
In this paper the superstability of the Cauchy equation can be proved for complex valued functions on commutative semigroup under some suitable conditions. Furthermore, in this note, we give a partial affirmative answer to problem 18, in the 31st ISFE. 相似文献
5.
关于耗散波动方程精确能控性的奇异极限的一个注记 总被引:1,自引:1,他引:0
本文在比文献[1]更一般的几何控制条件下,分析了具齐次Dirichlet边界条件的耗散波动方程精确能控性的奇异摄动问题.结论是由这类波动方程的精确能控性可得到热传导方程的精确零能控性. 相似文献
6.
A Note on the Numerical Solution of some Singular Second Order Differential Equations 总被引:1,自引:0,他引:1
In this note we present a method for the numerical solutionof linear second order differential equations with two pointboundary conditions for which there is a regular singularityat, or near to, a boundary point. An extension of the techniqueis used to solve a boundary value problem for a non-linear secondorder differential equation. 相似文献
7.
Marko Švec 《Annali di Matematica Pura ed Applicata》1967,77(1):179-191
Summary The aim of this note is to show that, under certain conditions, the comparìson theorems between a nonlinear second order differential
equation of certain type and a linear second order differential equation hold. From this we shall be able to guarentee the
oscillatory or nonoscillatory character of certain or all solutions of the considered nonlinear differential equation.
Work done at the Instituto Matematico ? Ulisse Dini ? in Firenze. 相似文献
8.
In this note, we study symmetry of solutions of the elliptic equation\begin{equation*} -\Delta _{\mathbb{S}^{2}}u+3=e^{2u}\ \ \hbox{on}\ \ \mathbb{S}^{2},\end{equation*} that arises in the consideration of rigidity problem of Hawking mass in general relativity. We provide various conditions under which this equation has only constant solutions, and consequently imply the rigidity of Hawking mass for stable constant mean curvature (CMC) sphere. 相似文献
9.
This note deals with a damped wave equation and the evolution of a Kelvin–Voigt viscoelastic material, both problems being subject to unilateral boundary conditions. The functional properties of all the traces are precisely identified through Fourier analysis, which implies the existence of a solution satisfying almost everywhere the unilateral boundary conditions. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
One of the main problems in the theory of orthogonal polynomials in several variables is the determination of partial differential equations which have the given polynomials as their solutions. In this note, we consider partial differential equations which are two-dimensional generalizations of the classical differential equation for the Chebyshev polynomials in one variable and we will give conditions for its polynomial solutions. In addition, we will be able to determine all polynomials of a given class which are solutions of the partial differential equation under consideration. In the last section, we establish a connection between the different polynomial solutions. 相似文献
11.
We consider a model initial-boundary value problem for the Benjamin-Bona-Mahony-Burgers equation with initial conditions having a physical meaning. We prove the unique local solvability in the classical sense and obtain sufficient conditions for blowup and an estimate of the blowup time. To prove the blowup, we use the known test function method developed in papers by V. A. Galaktionov, E. L. Mitidieri, and S. I. Pohozaev. We note that this is one of the first results toward the blowup for the considered equation. 相似文献
12.
In this note, we apply numerical analysis to the first equation, find the conditions for it to have oscillating solutions and therefore solve an open problem posed by Peter A. Clarkson. 相似文献
13.
In this paper, we consider whether or not the feedback control has influence on a nonlinear population equation with several time delays. The general criteria of integrable form on the permanence are established, and we note that the feedback control has no influence to the permanence of system. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global asymptotic stability of any positive solutions to the system. 相似文献
14.
A. E. Green P. M. Naghdi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(2):159-168
It is shown in this note that a general balance of entropy postulated previously with only a limited motivation (based on the form of the energy equation for an inviscid fluid) is consistent with, and can be derived from, a general balance of energy. In this derivation, an early form of entropy balance does not make use of invariance conditions under superposed rigid body motions. However, with the help of the latter invariance conditions, additional results are also derived which provide some insight on the structure of the basic equations in thermomechanics. 相似文献
15.
Josep M. Olm Xavier Ros-Oton Tere M. Seara 《Journal of Mathematical Analysis and Applications》2011,381(2):582-589
The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation x?x−1, and there are many results available in the literature for the first kind equation. However, the equivalence breaks down when one seeks for solutions with nonconstant sign. This note is devoted to periodic solutions with nonconstant sign in Abel equations of the second kind. Specifically, we obtain sufficient conditions to ensure the existence of a periodic solution that shares the zeros of the leading coefficient of the Abel equation. Uniqueness and stability features of such solutions are also studied. 相似文献
16.
Karam Allali 《Comptes Rendus Mathematique》2017,355(11):1148-1153
The existence and the uniqueness of solutions to a problem of miscible liquids are investigated in this note. The model consists of Navier–Stokes equations with Korteweg stress terms coupled with the reaction–diffusion equation for the concentration. We assume that the fluid is incompressible and the Boussinesq approximation is adopted. The global existence and uniqueness of solutions is established for some optimal conditions on the reaction source term and the external force functions. 相似文献
17.
Symmetry-based solution of a model for a combination of a risky investment and a riskless investment
Benth and Karlsen [F.E. Benth, K.H. Karlsen, A note on Merton's portfolio selection problem for the Schwartz mean-reversion model, Stoch. Anal. Appl. 23 (2005) 687-704] treated a problem of the optimisation of the selection of a portfolio based upon the Schwartz mean-reversion model. The resulting Hamilton-Jacobi-Bellman equation in 1+2 dimensions is quite nonlinear. The solution obtained by Benth and Karlsen was very ingenious. We provide a solution of the problem based on the application of the Lie theory of continuous groups to the partial differential equation and its associated boundary and terminal conditions. 相似文献
18.
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two different methods, respectively, based on variance computations and on path-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution. 相似文献
19.
为了研究可修复系统适定性和稳定性,首先利用Co半群理论,研究了Volterra方程的适定性和渐进行为.其次利用特征线法求得系统方程的时间依赖解,通过边界条件将其转化为有限维空间上的Volterra方程.最后,由所建立的Volterra方程的相关结果,得到了可修复系统的适定性和稳定性. 相似文献
20.
It is known since Galois that an algebraic equation can be solved using suitable nth roots whenever the corresponding Galois group is soluble. The object of this note is to construct real numbers with the use of the nth parts of suitable angles and to state necessary and sufficient conditions for this to be possible. 相似文献