Nonstationary Initial Boundary Value Contact Problems of Generalized Elastothermodiffusion
نویسنده
چکیده
The initial boundary value problems with mixed boundary conditions are considered for a system of partial differential equations of generalized electrothermodiffusion. Approximate solutions are constructed and a mathematical substantiation of the method is given. It is well known that a wide range of problems of mathematical physics includes boundary value and initial boundary value problems for differential equations. Such problems are rather difficult to solve because of an enormous variety of geometrical forms of the investigated objects and the complexity of boundary conditions. Hence an important and timely task has arisen to develop sufficiently effective methods and tools for solving the above-mentioned problems and obtaining their numerical solutions. Until recently no methods were known for solving problems of elasticity by means of conjugate fields. However, in the past few years there have appeared and keep on appearing numerous published works dedicated to this topic. The results of our studies in this direction are presented mainly in [1, 2, 3]. In this paper, using the generalized Green–Lindsay theory of elastothermodiffusion as an example, the approaches to the solution of nonstationary initial boundary value contact problems with mixed boundary conditions are described for a system of partial differential equations of this theory in a nonhomogeneous medium. These approaches are based on the method of discrete singularities known as the Riesz–Fischer–Kupradze method. The particular case is treated in [4]. 1991 Mathematics Subject Classification. 73B30, 73C25.
منابع مشابه
Three-dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions
We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [1–8], we prove theorems on the existence and uniqueness of t...
متن کاملSolutions of initial and boundary value problems via F-contraction mappings in metric-like space
We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...
متن کاملNon-stationary Problems of Generalized Elastothermodiffusion for Inhomogeneous Media
The method of investigation of non-stationary boundary value problems of the theory of thermodiffusion using the Laplace integral transform is described. In the classical theory of elasticity this method was first used by V. Kupradze and the author. The interconnection of deformation, thermal conductivity and diffusion processes in an elastic isotropic solid body is described by a system of fiv...
متن کاملBoundary Value Problems in Generalized Thermodiffusive Elastic Medium
In the present study, the boundary value problems in generalized thermodiffusive elastic medium has been investigated as a result of inclined load. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. As an application of t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001