共查询到20条相似文献,搜索用时 15 毫秒
1.
Praveen Agarwal Obidjon Kh.Abdullaev 《Mathematical Methods in the Applied Sciences》2020,43(6):3716-3726
This work devoted to prove of uniqueness and existence of solution of the nonlocal problem with integral gluing condition for the loaded parabolic-hyperbolic type equation involving Caputo derivatives which loaded parts in Riemann-Liouville integral-differential operator. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of integral equations. 相似文献
2.
For an equation of the parabolic-hyperbolic type, we consider an inverse problem with a nonlocal condition relating solution
derivatives that belong to different types of the equation in question. We justify a uniqueness criterion and prove the existence
of a solution of the problem by the spectral analysis method. We prove the stability of the solution with respect to the nonlocal
boundary condition. 相似文献
3.
For an equation of mixed type in a rectangular domain, we use spectral analysis to establish a uniqueness criterion for the solution of a problem with a nonlocal condition relating the values of the unknown solution that belong to different types of the considered equation. We prove the stability of the solution with respect to the nonlocal condition. 相似文献
4.
The present paper is devoted to the study of a boundary value problem for abstract first order linear differential equation with integral boundary conditions. We obtain necessary and sufficient conditions for the unique solvability and well-posedness. We also study the Fredholm solvability. Finally, we obtain a result of the stability of solution with respect to small perturbation. 相似文献
5.
A. V. Tarasenko 《Russian Mathematics (Iz VUZ)》2013,57(1):64-71
For a mixed-type equation we study a problem with generalized fractional integrodifferentiation operators in the boundary condition. We prove its unique solvability under inequality-type conditions imposed on the known functions for various orders of fractional integrodifferentiation operators. We prove the existence of a solution to the problem by reducing the latter to a fractional differential equation. 相似文献
6.
L. S. Pul’kina 《Differential Equations》2008,44(8):1119-1125
We consider a mixed initial-boundary value problem for a multidimensional (with respect to the space variables) hyperbolic equation with a nonlocal boundary condition containing an integral of the desired solution. We prove the unique solvability of the problem in the space W 2 1 . 相似文献
7.
L. S. Pul’kina 《Russian Mathematics (Iz VUZ)》2016,60(9):38-45
We consider an initial-boundary problem with dynamic nonlocal boundary condition for a pseudohyperbolic fourth-order equation in a cylinder. Dynamic nonlocal boundary condition represents a relation between values of a required solution, its derivatives with respect to spatial variables, second-order derivatives with respect to time variable and an integral term. The main result lies in substantiation of solvability of this problem. We prove the existence and uniqueness of a generalized solution. The proof is based on the a priori estimates obtained in this paper, Galyorkin’s procedure and the properties of the Sobolev spaces. 相似文献
8.
Alexander Gladkov Tatiana Kavitova 《Mathematical Methods in the Applied Sciences》2020,43(8):5464-5479
We prove the global existence and blow-up of solutions of an initial boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for large values of time. 相似文献
9.
Salah Boulaaras Abderrahmane Zaraï Alaeddin Draifia 《Mathematical Methods in the Applied Sciences》2019,42(8):2664-2679
In this paper, we are going to deal with the nonlocal mixed boundary value problem for the Moore‐Gibson‐Thompson equation. Galerkin method was the main used tool for proving the solvability of the given nonlocal problem. 相似文献
10.
This work is devoted to the investigation of the nonclassical problem for a multidimensional elliptic equation with two integral boundary conditions. By introducing special multipliers we prove the uniqueness of the solution and obtain new a priori estimates, which permit one to establish the existence of a solution in the corresponding Sobolev spaces. 相似文献
11.
K. B. Sabitov 《Differential Equations》2011,47(10):1490-1497
We consider the first boundary value problem for equations of mixed type in a rectangular domain. A criterion for the solution uniqueness is proved by the spectral expansion method. The solution is constructed in the form of a series in the eigenfunctions of the corresponding one-dimensional spectral problem. The stability of the solution with respect to the initial function is proved. 相似文献
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13.
We state a new nonlocal boundary value problem for a mixed parabolic-hyperbolic equation. The equation is of the first kind, i.e., the curve on which the equation changes type is not a characteristic. The nonlocal condition involves points in hyperbolic and parabolic parts of the domain. This problem is a generalization of the well-known Frankl-type problems. Unlike other close publications, the hyperbolic part of the domain agrees with a characteristic triangle. We prove unique solvability of this problem in the sense of classical and strong solutions. 相似文献
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15.
The spectral analysis method is used to establish a uniqueness criterion and prove the existence of a solution of the first initial-boundary value problem for a special equation of mixed type. 相似文献
16.
E. R. Mansurova 《Russian Mathematics (Iz VUZ)》2009,53(4):49-53
We prove the unique solvability of an analog of the Tricomi problem for an elliptic-hyperbolic equation with a nonlocal integral conjugate condition on the characteristic line. 相似文献
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19.
Alexander Gladkov Mohammed Guedda 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(13):4573-4580
In this paper we consider a semilinear parabolic equation ut=Δu−c(x,t)up for (x,t)∈Ω×(0,∞) with nonlinear and nonlocal boundary condition u∣∂Ω×(0,∞)=∫Ωk(x,y,t)uldy and nonnegative initial data where p>0 and l>0. We prove some global existence results. Criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given. 相似文献
20.
A. M. Denisov 《Proceedings of the Steklov Institute of Mathematics》2013,282(1):80-89
We investigate a multitype Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Assuming that the mean of the increment X of the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices is negative and the random variable Xe X has zero mean, we find the asymptotics of the survival probability at time n as n → ∞. 相似文献