共查询到20条相似文献,搜索用时 0 毫秒
1.
Siberian Mathematical Journal - Under study is the unique solvability of a Cauchy type problem and a generalized Schowalter–Sidorov type problem for a class of linear inhomogeneous equations... 相似文献
2.
《偏微分方程通讯》2013,38(11-12):1653-1695
Abstract An initial boundary-value problem in a half-strip with one boundary condition for the Korteweg–de Vries equation is considered and results on global well-posedness of this problem are established in Sobolev spaces of various orders, including fractional. Initial and boundary data satisfy natural (or close to natural) conditions, originating from properties of solutions of a corresponding initial-value problem for a linearized KdV equation. An essential part of the study is the investigation of special solutions of a “boundary potential” type for this linearized KdV equation. 相似文献
3.
By reflections, we obtain the Schwarz?CPoisson formula in a sector with angle ${\vartheta=\frac{\pi}{n},\,n\in \mathbb{N}}$ , which is a generalization of the corresponding result obtained by Begehr and Vaitekhovich (Funct Approx 40(2):251?C282, 2009). Especially, boundary behaviors at corner points are discussed in detail. Then we consider the Schwarz and Dirichlet boundary-value problems (BVPs) for the Cauchy?CRiemann equation, and expressions of solution and the condition of solvability are explicitly obtained. 相似文献
4.
F. G. Khushtova 《Russian Mathematics (Iz VUZ)》2017,61(7):73-82
We investigate the second boundary-value problem in the half-strip for a parabolic equation with the Bessel operator and Riemann–Liouville partial derivative. In terms of the integral transformation with theWright function in the kernel, we find the representation of a solution in the case of zero edge condition. We prove the uniqueness of a solution in the class of functions satisfying an analog of the Tikhonov condition. 相似文献
5.
We study the unique solvability of the Cauchy and Schowalter–Sidorov type problems in a Banach space for an evolution equation with a degenerate operator at the fractional derivative under the assumption that the operator acting on the unknown function in the equation is p-bounded with respect to the operator at the fractional derivative. The conditions are found ensuring existence of a unique solution representable by means of the Mittag-Leffler type functions. Some abstract results are illustrated by an example of a finite-dimensional degenerate system of equations of a fractional order and employed in the study of unique solvability of an initial-boundary value problem for the linearized Scott-Blair system of dynamics of a medium. 相似文献
6.
In this paper, we study necessary conditions for the existence and uniqueness of continuous solution for a nonlocal boundary value problem with nonlinear term involving Riemann–Liouville fractional derivative. Our results are based on Schauder fixed point theorem and the Banach contraction principle fixed point theorem. Examples illustrating the obtained results are also presented. 相似文献
7.
In this work we study the existence of a solution for the problem ? Δ p u = f(u) + tΦ(x) + h(x), with homogeneous Dirichlet boundary conditions. Here the nonlinear term f(u) is a so-called jumping nonlinearity. In the proofs we use topological arguments and the sub-supersolutions method, together with comparison principles for the p-Laplacian. 相似文献
8.
F. G. Khushtova 《Mathematical Notes》2016,99(5-6):916-923
The first boundary-value problem in the half-strip for a parabolic-type equation with Bessel operator and Riemann–Liouville derivative is studied. In the case of the zero initial condition, the representation of the solution in terms of the Fox H-function is obtained. The uniqueness of the solution for a class of functions vanishing at infinity is proved. It is shown that when the equation under consideration coincides with the Fourier equation, the obtained representation of the solution becomes the known representation of the solution of the corresponding problem. 相似文献
9.
In this work, we are mainly concerned with the existence of positive solutions for the fractional boundary-value problem $$ \left\{ {\begin{array}{*{20}{c}} {D_{0+}^{\alpha }D_{0+}^{\alpha }u=f\left( {t,u,{u}^{\prime},-D_{0+}^{\alpha }u} \right),\quad t\in \left[ {0,1} \right],} \hfill \\ {u(0)={u}^{\prime}(0)={u}^{\prime}(1)=D_{0+}^{\alpha }u(0)=D_{0+}^{{\alpha +1}}u(0)=D_{0+}^{{\alpha +1}}u(1)=0.} \hfill \\ \end{array}} \right. $$ Here ?? ?? (2, 3] is a real number, $ D_{0+}^{\alpha } $ is the standard Riemann?CLiouville fractional derivative of order ??. By virtue of some inequalities associated with the fractional Green function for the above problem, without the assumption of the nonnegativity of f, we utilize the Krasnoselskii?CZabreiko fixed-point theorem to establish our main results. The interesting point lies in the fact that the nonlinear term is allowed to depend on u, u??, and $ -D_{0+}^{\alpha } $ . 相似文献
10.
V. V. Karachik 《Differential Equations》2018,54(5):648-657
We obtain necessary and sufficient conditions for the solvability of the Riquier–Neumann problem for the inhomogeneous polyharmonic equation in the unit ball. 相似文献
11.
Xue Yang 《Journal of Optimization Theory and Applications》2012,152(3):814-822
This paper is concerned with the existence and uniqueness of solutions to the Sturm–Liouville boundary value problem across
resonance. By using optimal control theory, we present some global optimality results about the unique solvability for the
Sturm–Liouville problem. 相似文献
12.
13.
Delphine Salort 《偏微分方程通讯》2013,38(2):209-228
We consider some linear Schrödinger equation with variable coefficients associated to a smooth symmetric metric g which can be degenerate, without sign and such that g has a submatrix of fixed rank v which is uniformly nondegenerate. In this general setting we prove Strichartz estimates with a loss of derivative on the solution. We also discuss the problem of the control of high frequencies. In particular, we prove that if the equation preserves the H s norm for all s ≥ 0, then we obtain almost the same Strichartz estimates as those for the Schrödinger equation associated to a Riemannian metric of dimension 2d ? v. 相似文献
14.
In this paper we consider a kind of Riemann boundary value problem (for short RBVP) for null solutions to the iterated generalized Cauchy–Riemann operator and the polynomially generalized Cauchy–Riemann operator, on the sphere of ${\mathbb{R}^{n+1}}$ with Hölder-continuous boundary data. Making full use of the poly-Cauchy type integral operator in Clifford analysis, we give explicit integral expressions of solutions to this kind of boundary value problems over the sphere of ${\mathbb{R}^{n+1}}$ . As special cases solutions of the corresponding boundary value problems for the classical poly-analytic and meta-analytic functions are also derived, respectively. 相似文献
15.
A model spectral problem of the form -i)y+xy= y on the finite interval [-1,1] with the Dirichlet boundary conditions is considered. Here is the spectral parameter and is positive. The behavior of the spectrum of this problem as 0 is completely investigated. The limit curves are found to which the eigenvalues concentrate and the counting eigenvalue functions along these curves are obtained. 相似文献
16.
The following Riemann–Hilbert problem is solved: find an analytical function <> from the Smirnov class E
p(D), whose angular boundary values satisfy the condition
The boundary of the domain D is assumed to be a piecewise smooth curve whose nonintersecting Lyapunov arcs form, with respect to D, the inner angles with values , 0 < 2. 相似文献
17.
In this paper, we derive the existence and uniqueness of mild solutions for inhomogeneous fractional evolution equations in Banach spaces by means of the method of fractional resolvent. Furthermore, we give the necessary and sufficient conditions for the existence of strong solutions. An example of the fractional diffusion equation is also presented to illustrate our theory. 相似文献
18.
Chuan-Fu Yang 《Complex Analysis and Operator Theory》2013,7(4):1185-1196
The sum of the eigenvalues {λ n } of an operator is usually called its trace. For the eigenvalues λ n of an differential operator, the series ${\sum_n \lambda_n}$ , generally speaking, diverges; however, it can be regularized by subtracting from λ n the first terms of the asymptotic expansion, which interfere with the convergence of the series. The sum of such a regularized series is called the trace. In this work, we consider the spectral problem for Sturm–Liouville differential operator on d-star-type graph with a Kirchhoff-type condition in the internal vertex, where the integer d ≥ 2. Regularized trace formula of this operator is established with residue techniques in complex analysis. 相似文献
19.
Justin Holmer 《偏微分方程通讯》2013,38(8):1151-1190
We prove local well-posedness of the initial-boundary value problem for the Korteweg–de Vries equation on right half-line, left half-line, and line segment, in the low regularity setting. This is accomplished by introducing an analytic family of boundary forcing operators. 相似文献
20.
In this paper, we are concerned with Cauchy problems of fractional differential equations with Riemann–Liouville fractional derivatives in infinite-dimensional Banach spaces. We introduce the notion of fractional resolvent, obtain some its properties, and present a generation theorem for exponentially bounded fractional resolvents. Moreover, we prove that a homogeneous α-order Cauchy problem is well posed if and only if its coefficient operator is the generator of an α-order fractional resolvent, and we give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of an inhomogeneous α-order Cauchy problem. 相似文献