Численное моделирование процессов теплопроводности с градиентной нелинейностью»

Аннотация

Subjects of research: quasilincar parabolic equations with the gradient nonlinearity, describing nonlinear processes heat conductivity. Purpose of work: the research of qualitative properties solutions of nonlinear mathematical models, in homogeneous and heterogeneous environment, when coefficient heat conductivity depends on a gradient of temperature, in view of absorption or source. Methods of research: algorithm of nonlinear splitting, technique of comparison of the solutions, iterative numerical methods, method of variable directions and proracc method. The results obtained and their novelty: for the quasilincar parabolic equations with the gradient nonlinearity of the second order develops of asymptotic theory based on a method of nonlinear splitting. The estimations of the decisions problem of Cauchy by algorithm of nonlinear splitting for the nonlinear heat conductivity equation with strong absorption divergent and non divergent types arc received. Asymptotic behavior of the solution in a critical ease is investigated. The conditions of occurrence of the unlimited solutions for the equation with a nonlinear source in heterogeneous media are received. Basing on the received estimations of the solutions and fronts, the computing experiments with use MathCad is carried out. Practical value: results of the dissertation have theoretical character. Degree of embed and economic efficiency: the results of the dissertation can be used in modeling nonlinear problems of mathematical physics and further in developing on the theory of nonlinear parabolic equations. Field of application: the results of the dissertation can be used in modeling nonlinear processes heat conductivity, filtration, diffusion and on the base of achieved results, the special courses for students can be tcachcd.