Presently there is a little information that relates to heat shield systems.  Also this information is not certain in so many cases.  The main reason is that accurate calculations for measuring the sacrificing rate of various materials have not been obtained yet.  Additionally, the real scale test has two disadvantages: high cost and low flexibility, and for each case we must perform a new test...

A Langevin equation with variable drift and diffusion coefficients separable in time and space and its corresponding Fokker-Planck equation in the Stratonovich approach are considered. From this Fokker-Planck equation a class of exact solutions with the same spatial drift and diffusion coefficients is obtained. Furthermore, some details of this system are analyzed by using the spatial diffusion...

‎this paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎at first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎then its adjoint problem is calculated‎. ‎after that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎finally the convergence ...

the momentum equation in the kinematic wave model is a power-law equation with two parameters. these parameters, which relate the discharge to the flow area, are commonly derived using manning’s equation. in general, the values of these parameters depend on the flow depth except for some special cross sections. in this paper, improved estimates of the kinematic wave parameters for circular chan...

We study separability properties of solutions of elliptic equations with piecewise constant coefficients in R d , d ≥ 2. Besides that, we develop efficient tensor-structured preconditioner for the diffusion equation with variable coefficients. It is based only on rank structured decomposition of the tensor of reciprocal coefficient and on the decomposition of the inverse of the Laplacian operat...