共查询到20条相似文献,搜索用时 109 毫秒
1.
K. B. Sabitov 《Differential Equations》2011,47(5):706-714
For a third-order differential equation of parabolic-hyperbolic type, we suggest a method for studying the first boundary
value problem by solving an inverse problem for a second-order equation of mixed type with unknown right-hand side. We obtain
a uniqueness criterion for the solution of the inverse problem. The solution of the inverse problem and the Dirichlet problem
for the original equation is constructed in the form of the sum of a Fourier series. 相似文献
2.
We consider a problem for a quasilinear hyperbolic equation with a nonlocal condition that contains a retarded argument. By reducing this problem to a nonlinear integrofunctional equation, we prove the existence and uniqueness theorem for its solution. We pose an inverse problem of finding a solution-dependent coefficient of the equation on the basis of additional information on the solution; the information is given at a fixed point in space and is a function of time. We prove the uniqueness theorem for the solution of the inverse problem. The proof is based on the derivation and analysis of an integro-functional equation for the difference of two solutions of the inverse problem. 相似文献
3.
E. F. Lelikova 《Proceedings of the Steklov Institute of Mathematics》2013,281(1):95-104
We study the asymptotic behavior of a solution of the first boundary value problem for a second-order elliptic equation in a nonconvex domain with smooth boundary in the case where a small parameter is a factor at only some of the highest derivatives and the limit equation is an ordinary differential equation. Although the limit equation has the same order as the initial equation, the problem is singulary perturbed. The asymptotic behavior of its solution is studied by the method of matched asymptotic expansions. 相似文献
4.
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
5.
We consider a linear integral equation with a hypersingular integral treated in the sense of the Hadamard finite value. This
equation arises in the solution of the Neumann boundary value problem for the Laplace equation with a representation of a
solution in the form of a double-layer potential. We consider the case in which the interior or exterior boundary value problem
is solved in a domain; whose boundary is a smooth closed surface, and an integral equation is written out on that surface.
For the integral operator in that equation, we suggest quadrature formulas like the method of vortical frames with a regularization,
which provides its approximation on the entire surface for the use of a nonstructured partition. We construct a numerical
scheme for the integral equation on the basis of suggested quadrature formulas, prove an estimate for the norm of the inverse
matrix of the related system of linear equations and the uniform convergence of numerical solutions to the exact solution
of the hypersingular integral equation on the grid. 相似文献
6.
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
7.
8.
In this article we study the homogenization of an optimal control problem for a parabolic equation in a domain with highly oscillating boundary. We identify the limit problem, which is an optimal control problem for the homogenized equation and with a different cost functional. 相似文献
9.
51.Introducti0nSince198O)stheoriesandapplicationsofboundaryelementmethods(BEM)orboundaryintegralmethods(BIM)havemadegreatsuccessesfortheparaboliclnit1alboundaryvalueproblems(seeL1-12j),andtheapproachhasbeenappliedtonumericalsolutionsofinitialboundaryva1ueproblemssuccessfully(seeL1-5j'L8j).Thepropertiesofboundaryelementoperatorshavebeenstudiedbyboundaryintegralmethodsbymanyauthors(see.[4j,L6J'[7j'L12J).Theseresultsprovideabasisforconvergencesanderrorestimatesfornumericalapproximationofbou… 相似文献
10.
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
11.
The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous nonlinear Landau equation with Maxwellian molecules and inhomogeneous linear Fokker-Planck equation to show the ultra-analytic effects of the Cauchy problem. Those smoothing effect results are optimal and similar to heat equation. In the second part, we study a model of spatially inhomogeneous linear Landau equation with Maxwellian molecules, and show the analytic effect of the Cauchy problem. 相似文献
12.
Some exact solutions to a nonlinear heat equation are constructed. An initial-boundary value problem is examined for a nonlinear heat equation. To construct solutions, the problem for a partial differential equation of the second order is reduced to a similar problem for a first order partial differential equation. 相似文献
13.
Zhousheng Ruan 《Applicable analysis》2017,96(10):1638-1655
In this paper, we study an inverse problem of identifying a time-dependent term of an unknown source for a time fractional diffusion equation using nonlocal measurement data. Firstly, we establish the conditional stability for this inverse problem. Then two regularization methods are proposed to for reconstructing the time-dependent source term from noisy measurements. The first method is an integral equation method which formulates the inverse source problem into an integral equation of the second kind; and a prior convergence rate of regularized solutions is derived with a suitable choice strategy of regularization parameters. The second method is a standard Tikhonov regularization method and formulates the inverse source problem as a minimizing problem of the Tikhonov functional. Based on the superposition principle and the technique of finite-element interpolation, a numerical scheme is proposed to implement the second regularization method. One- and two-dimensional examples are carried out to verify efficiency and stability of the second regularization method. 相似文献
14.
A problem with free (unknown) boundary for a one-dimensional diffusion-convection equation is considered. The unknown boundary is found from an additional condition on the free boundary. By the extension of the variables, the problem in an unknown domain is reduced to an initial boundary-value problem for a strictly parabolic equation with unknown coefficients in a known domain. These coefficients are found from an additional boundary condition that enables the construction of a nonlinear operator whose fixed points determine a solution of the original problem.
相似文献15.
《Journal of Computational and Applied Mathematics》1988,24(3):293-318
Two different numerical models are constructed to solve a two dimensional subsidence mound problem heated along the moving wet/dry interface. One numerical model is based on cartesian coordinates while the other is based on polar coordinates. In both approaches coordinate transformations are used that render the interface stationary. The problem involves a system of three coupled equations; an elliptic equation for a stream function, a parabolic equation for the temperature and a non-linear equation for the boundary location. Good agreement is found between the results of both methods. Graphic results are presented for the decay of a subsidence mound for different values of the various parameters in the model problem. 相似文献
16.
A. I. Kolosov 《Mathematical Notes》1971,9(1):45-48
An investigation of a boundary-value problem on a half-line for a nonlinear ordinary second order differential equation whose free term has a discontinuity in a strip. A method is proposed for the transformation of the boundary-value problem into an integral equation with a discontinuous operator. Some results have recently been obtained concerning the existence, the comparison, and integral representations of solutions of this integral equation.Translated from Matematicheskie Zematki, Vol. 9, No. 1, pp. 77–82, January, 1971. 相似文献
17.
A.S. Berdyshev 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(6):3268-3273
In the present work, a non-local boundary value problem with special gluing conditions for a mixed parabolic-hyperbolic equation with parameter is considered. The parabolic part of this equation is a fractional analogue of heat equation and the hyperbolic part is the telegraph equation. The considered problem is reduced, for positive values of the parameter, to an equivalent system of the second kind Volterra integral equations. Due to the influence of the fractional diffusion equation, the looked for solution belongs to a specific class of functions. The method of the Green functions and the properties of integro-differential operators are on the basis of the investigation. 相似文献
18.
P. Vyridis 《Journal of Mathematical Sciences》2001,106(3):2919-2924
Necessary and sufficient conditions for bifurcation in a variational problem on a one-dimensional closed manifold are obtained. In local coordinates, this problem corresponds to a semilinear 4th-order differential equation and can be regarded as a model equation of problems in the theory of shells. Bibliography: 5 titles. 相似文献
19.
We establish a weak solvability of the initial-boundary value problem for a dynamic model of thermoviscoelasticity. The problem under consideration is an extension of the Jeffreys model obtained with the help of a consequence of the energy balance equation. We study the corresponding initial-boundary value problem by splitting the problem and reducing it to an operator equation in a suitable Banach space. 相似文献
20.
A. A. Abashkin 《Russian Mathematics (Iz VUZ)》2013,57(6):1-9
We study a boundary-value problem for a generalized biaxisymmetric Helmholtz equation. Boundary conditions in this problem depend on equation parameters. By the method of separation of variables, using the Fourier-Bessel series expansion and the Hankel transform, we prove the unique solvability of the problem and establish explicit formulas for its solution. 相似文献