Examples of using Boundary value in English and their translations into Danish
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He is famed for solving a variety of boundary value problems.
Petrovsky also worked on the boundary value problem for the heat equation and this was applied to both probability theory and work of Kolmogorov.
Also in 1969 he published The weak Newton method and boundary value problems.
His doctoral dissertation Some Problems in the Boundary Value Theory of Linear Differential Equations was supervised by Waldemar Trjitzinsky.
He introduced the concept of a well-posed initial value and boundary value problem.
And then submitted his thesis in 1917 on boundary value problems for linear differential equations.
These ideas in the main concern generalised solutions of non-classical boundary value problems.
Krylov improved Fourier 's method for solving boundary value problems in a 1905 paper and gave many applications.
Among the topics he considered were elasticity, geometrical optics,hydrodynamics and boundary value problems.
Another major text which he published was Mixed boundary value problems in potential theory in 1966.
In order to proceed further it is necessary to limit W to functions which are solutions to the boundary value problem.
The book deals with, among other topics, Laplace 's equation,mixed boundary value problems, the wave equation, and the heat equation.
His work on boundary value problems on differential equations is remembered because of what is called today Sturm-Liouville theory which is used in solving integral equations.
The book concludes with chapters which bring together many results from Sneddon's own papers on boundary value problems in elasticity.
Reports on methods of solving nonlinear boundary value problems for partial differential equations, on a theoretical and functional analysis basis.
He took written examinations in 1912 and 1913. andthen submitted his thesis in 1917 on boundary value problems for linear differential equations.
His research during this period continued on boundary value problems, but also included advances in mathematical physics, differential equations, and approximations.
It was developed during several decades andwas seen as a universal tool with which it was possible to solve the majority of boundary value problems of physics.
The work of Valentina Borok and her school on boundary value problems in layers forms an important chapter in the general theory of partial differential equations.
Some of his later papers examine numerical methods for factorising polynomials, for solving elliptic partial differential equations, andmethods for treating singularities in boundary value problems.
It investigated in detail Cauchy-type integrals which played an important role in boundary value problems in the theory of functions of a complex variable.
He worked on the general theory of boundary value problems for linear systems of partial differential equations of elliptic type,finding general methods of solving boundary value problems.
While working in Moscow,Sobolev built on the standard variational method for solving elliptic boundary value problems by introducing these Sobolev function spaces.
His research concentrated on asymptotic expansions, boundary value problems, and Sturm- Liouville type problems but his thesis advisor Eliakim Moore appears to have been a less influential guide to Birkhoff than was Poincaré.
In addition to the work for his master's thesis and his doctoral thesis referred to above,he reduced problems to boundary value problems of Dirichlet type where Laplace's equation must be solved on a surface.
In the following year she published On some boundary value problems in the theory of the non-uniform supersonic motion of an aerofoil in which she gives rigorous proofs of methods to find the velocity potential due to a two-dimensional airfoil in a supersonic stream whose shape and motion are given.
L Cesari, reviewing this important work,writes that Lions:… reports on methods of solving nonlinear boundary value problems for partial differential equations, on a theoretical and functional analysis basis.
In a series of three significant papers in the late 1950s, Cathleen Morawetz used functional analysis coupled with ingenious new estimates for an equation of mixed type, i.e. with both elliptic and hyperbolic regions,to prove a striking new theorem for boundary value problems for partial differential equations.
It covers topics such as: vectors and matrices;Fourier series; boundary value problems; Legendre and Bessel functions; integral equations; the calculus of variations and dynamics; and the operational calculus.
It is a major text containing around 550 pages andis mainly concerned with applications which involve the solution of ordinary differential equations, and boundary value and initial value problems for partial differential equations.