共查询到20条相似文献,搜索用时 15 毫秒
1.
G. R. Yunusova 《Differential Equations》2013,49(3):395-398
For an equation of the mixed elliptic-hyperbolic type, we study the inverse problem with a nonlocal condition relating the derivatives of the solution on the elliptic and hyperbolic parts of the boundary. We prove a uniqueness criterion and construct the solution in the form of a Fourier series. 相似文献
2.
Z. A. Nakhusheva 《Differential Equations》2013,49(10):1299-1306
We study a nonlocal interior-boundary value problem with an Erdelyi-Kober operator for the Lavrent’ev-Bitsadze equation and its analogs in the theory of equations of mixed parabolic-hyperbolic type. 相似文献
3.
T. E. Moiseev 《Differential Equations》2009,45(10):1547-1549
We study the existence of a regular (classical) solution of the Tricomi problem for the Lavrent’ev-Bitsadze equation with mixed boundary conditions. We find conditions under which the homogeneous problem has only the zero solution and give an example in which the homogeneous Tricomi problem has a nonzero solution. We also study the solvability of the inhomogeneous Tricomi problem. 相似文献
4.
We study the inverse problem for the Lavrent’ev-Bitsadze equation in a rectangular domain. We construct its solution as a series of eigenfunctions for the corresponding problem on eigenvalues and establish a criterion for its uniqueness. We also prove the stability of the obtained solution. 相似文献
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6.
T. E. Moiseev 《Differential Equations》2012,48(10):1433-1435
We study the solvability of the Gellerstedt problem for the Lavrent??ev-Bitsadze equation under an inhomogeneous boundary condition on the half-circle of the ellipticity domain of the equation, homogeneous boundary conditions on external, internal, and parallel side characteristics of the hyperbolicity domain of the equation, and the transmission conditions on the type change line of the equation. 相似文献
7.
Properties of solutions of the Tricomi problem for the Lavrent’ev-Bitsadze equation at corner points
A. V. Rogovoy 《Differential Equations》2013,49(12):1650-1654
We consider the Tricomi problem for the Lavrent’ev-Bitsadze equation for the case in which the elliptic part of the boundary is part of a circle. For the homogeneous equation, we introduce a new class of solutions that are not continuous at the corner points of the domain and construct nontrivial solutions in this class in closed form. For the inhomogeneous equation, we introduce the notion of an n-regular solution and prove a criterion for the existence of such a solution. 相似文献
8.
A. P. Soldatov 《Proceedings of the Steklov Institute of Mathematics》2012,278(1):233-240
The existence and uniqueness issues are discussed for several boundary value problems with Dirichlet data for the Lavrent’ev-Bitsadze equation in a mixed domain. A general mixed problem (according to Bitsadze’s terminology) is considered in which the Dirichlet data are relaxed on a hyperbolic region of the boundary inside a characteristic sector with vertex on the type-change interval. In particular, conditions are pointed out under which the problem is uniquely solvable for any choice of this vertex. 相似文献
9.
Z. A. Nakhusheva 《Differential Equations》2009,45(8):1223-1228
In a special rectangular domain, for a second-order linear equation of mixed type with discontinuous coefficients and with
the Lavrent’ev-Bitsadze operator in the leading part, we prove an extremum principle and existence and uniqueness theorems
for the solution of a nonlocal problem stated by A.A. Dezin in his report at the Joint Soviet-American Symposium on Partial
Differential Equations (Novosibirsk, 1963). 相似文献
10.
T. K. Yuldashev 《Russian Mathematics (Iz VUZ)》2016,60(9):53-60
We consider the problem on the unique solvability of the inverse problem for a nonlinear partial Benney–Luke type integro-differential equation of the fourth order with a degenerate kernel. We modify the degenerate kernelmethod which has been designed for Fredholm integral equations of the second kind to apply to the case of the above-mentioned equation. We exploit the Fouriermethod of separation of variables. By means of designations, the Benney–Luke type integro-differential equation is reduced to a system of algebraic equations. Using an additional condition, we obtain the countable system of nonlinear integral equations with respect to the main unknown function. We employ the method of successive approximations together with the contraction mapping principle. Finally, the restore function is defined. 相似文献
11.
We study the problem with boundary conditions of the first and second kind on the boundary of a rectangular domain for an equation with two internal perpendicular lines of change of a type. With the use of the spectral method we prove the unique solvability of the mentioned problem. The eigenvalue problem for an ordinary differential equation obtained by separation of variables is not self-adjoint, and the system of root functions is not orthogonal. We construct the corresponding biorthogonal system of functions and prove its completeness. This allows us to establish a criterion for the uniqueness of the solution to the problem under consideration. We construct the solution as the sum of the biorthogonal series. 相似文献
12.
S. A. Aldashev 《Russian Mathematics (Iz VUZ)》2011,55(4):1-4
We obtain a criterion for the unique solvability of the spectral problem in a cylindrical domain for a multidimensional Lavrent’ev-Bitsadze equation. 相似文献
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We consider an inverse problem of determining a spatially varying factor in a source term in the non-stationary linearized Navier–Stokes equations by observation data in an arbitrarily fixed sub-domain over some time interval. We prove the Lipschitz stability provided that the t-dependent factor satisfies a non-degeneracy condition. Our proof is based on a new Carleman estimate for the linearized Navier–Stokes equations. 相似文献
15.
R. V. Brizitskii A. S. Savenkova 《Computational Mathematics and Mathematical Physics》2010,50(6):984-992
The problem is studied of recovering the impedance function involved multiplicatively in boundary conditions for Maxwell’s
equations. The inverse problem is reduced to an extremum one. The solvability of the extremum problem is proved, an optimality
system is derived, and sufficient conditions for the local uniqueness and stability of its solution are established. 相似文献
16.
We study a boundary-value problem with Bitsadze–Samarskii conditions on boundary characteristic on a special inner curve and on a segment of degeneration of mixed type equation. Its solvability is proved by method of integral equations, and uniqueness of solution is established by means of the maximum principle. 相似文献
17.
《Comptes Rendus Mathematique》2008,346(11-12):635-640
18.
Xiaosheng Li 《Journal of Differential Equations》2012,253(2):694-726
In this work we consider the inverse boundary value problem for Schrödinger equations with Yang–Mills potentials in the domain of infinite slab type. We prove that the potentials can be determined uniquely up to a gauge equivalent class assuming that only partial measurements are known on the boundary hyperplanes. 相似文献
19.
Serik A. Aldashev 《Journal of Mathematical Sciences》2013,188(2):71-76
It is shown that the Dirichlet problem in a multidimensional domain for the Lavrent’ev–Bitsadze equation is uniquely solvable. A criterion of the uniqueness of the solution is obtained. 相似文献
20.
We consider a mixed boundary problem for the Navier–Stokes equations in a bounded Lipschitz two-dimensional domain: we assign a Dirichlet condition on the curve portion of the boundary and a slip zero condition on its straight portion. We prove that the problem has a solution provided the boundary datum and the body force belong to a Lebesgue’s space and to the Hardy space respectively. 相似文献