Evolution Equations and Lagrangian Coordinates

ISBN: 9783110148756 出版年：2011 页码：328 Meirmanov, Anvarbek M ,Pukhnachov, Vladislav V ,Shmarev, Sergei I De Gruyter

The Verigin problem: review of results filtration in a porous soil formulation of the problem self-similar solutions Stefan's problem as a limit case of Verigin's problem one-dimensional problem - main statements and formulation of results proofs of theorems 5.1, 5.2 - Verigin's problem with the given mass flux on the known boundaries and the Cauchy-Verigin problem proof of theorem 5.3 Verigin's problem with the given pressure on the known boundaries. equivalence transformations of evolution equations: main ideas a historical survey reciprocity transformations of second-order equations hidden symmetry of evolution equations linearization by means of Lagrangian coordinates Lagrange-invariant equations equations with spherical and cylindrical symmetries equivalence transformations for higher-order equations and systems of equations a remarkable equation of nonlinear heat conduction the on-phase Stefan problem - explicit solutions with functional arbitrariness. One dimensional parabolic equations: introduction Lagrangian coordinates in one-dimensional evolution equations analysis of the problem in Langragian terminology uniform estimates the inverse transformation some starting properties of the interface estimates for the time derivatives and the higher-order derivatives the interface regularity regularity of interfaces for a generalized porous medium equation axially symmetrical solutions of the porous medium equation - long-time asymptotic behaviour a non-classical problem for a degenerate parabolic equation - uniqueness of unbounded solutions the Stefan problem with degeneracy at the free boundary - example of exact solution. Parabolic equations in several space dimensions: review of results Langragian coordinates in the one-phase Stefan problem correctness of the linear model similarity solutions of the Stefan problem solvability of the nonlinear problem canonical Lagrangian coordinates Boussinesq's equation in filtration theory local regularity of interfaces bibliography notation.