Sentence examples for mixed boundary problem from inspiring English sources
In Section 6, we present the solution of the mixed boundary problem via an integral equation method.
The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically.
Zaremba wrote in [13] that it was Wirtinger who pointed out to him the great practical importance of this mixed boundary problem.
Very recently, for mixed boundary problem (1.1 - 1.4 1.1 - 1.4eralized Lewithfunctions, Fangeneralized25] proved the existence and uniqueness of gLewis solution and the energy functionsl decays exponentially or polynomially to zero as the time tends to inFangty by the technique of Lyandnov functional.
In [7], by using a fixed point theorem, the existence of at least three solutions for a mixed boundary problem with the equation ( | u ′ | p − 2 u ′ ) ′ = q ( x ) f ( u ) is obtained, by requiring, among other things, the boundness of f in a right neighborhood of zero (hypothesis (H6), Theorem 3.1), instead in our results (Theorems 3.5 and 3.6) the nonlinearity can blow up at zero.
The complicated mixed boundary problems of equations of heat conduction and elasticity are converted analytically into singular integral equations, which are solved numerically.
Comprehensive tests on several important applications are provided, such as Navier Stokes equations on irregular domains with traction boundary conditions, interface problems in incompressible flows, mixed boundary problems, and free boundary problems.
Compared with the Dirichlet problem, the mixed boundary value problem nablabigl[phi(Delta u_{k} bigr]=lambda f k, u_{k}, Delta u_{k}), quad kin[2, n-1]_{mathbb{Z}}, qquad u_{1}=0=Delta u_{n-1} (13) is less studied in the related literature.
Problem (1.1) is a mixed boundary value problem, and is different from the classical ones.
The mixed boundary value problem can be reduced to an RH problem as follows.
The reduction of the mixed boundary value problem to the form of the RH problem is given in Section 5.
