For an equation of mixed parabolic-hyperbolic type in a rectangular parallelepiped, the inverse problem of finding the factors of the right-hand side that depend on spatial variables is investigated. A criterion for the uniqueness of a solution is established. The solution is constructed as a ...
In this paper, for a two-dimensional wave equation in a rectangular parallelepiped, the Dirichlet problem. A uniqueness criterion is established. The solution is constructed as the sumof an orthogonal series. When justifying the convergence of a series, the problem of small denominators of two na...
Figure 3.11 shows a rectangular parallelepiped controlvolume described in rectangular Cartesian coordinates x, y, z, together with the mass fluxes through the six faces associated with the three associated components of the velocity vector u, v, w. In analogue to Eq. (3.8), conservation of ...
The paper discusses the regularity of solution of the mixed boundary value problem for elliptic partial differential equations on a rectangular parallelepiped by a priori estimate method, gives results about some additoinal regularity properties. 利用先验估计方法,讨论长方体上椭圆偏微分方程混杂问题解的...
The paper discusses the regularity of solution of the mixed boundary value problem forelliptic partial differential equations on a rectangular parallelepiped by a priori estimate method, gives results about some additoinal regularity properties.
Using ideas of conversion from polar to rectangular form and vector addition, waves of the same frequency can be easily combined. 7. Unit vectors have length 1. To find the unit vector in the same direction as a vector r divide the vector by its length: rˆ = r|r|. 8. Any ...
b. What type of surface is S_2? c. Find a vector function \ve find the rectangular equation for the surface by eliminating the parameters from the vector-valued function r(u,v)=ui+vj+ \frac{v}{2k} Consider the surface 4x2 + 16y2 +1z2 = 21 and the point P=(1...
For an inhomogeneous three-dimensional equation of mixed parabolic-hyperbolic type in a rectangular parallelepiped, the initial-boundary problem is studied. A criterion for the uniqueness of a solution is established. The solution is constructed as the sum of an orthogonal series. In substantiating ...
Establishes a uniform convergence of a difference solution to the Dirichlet problem for the Laplace equation on a rectangular parallelepiped, which is of the second order with respect to a grid step. Definition of the problem; Auxiliary lemmas; Proof of theorems.Volkov...
finite parallelepiped/ A2820H Neutron diffusionA solution to the integro-differential Boltzmann equation, which governs the steady-state space-angle distribution of the flux of monoenergetic neutrons in a rectangular parallelepiped of an isotropically scattering material, is presented. Results for both ...