Non-classical equations of mixed type and their applications in gas dynamics
The book contains the author's results on solvability of boundary value problems for linear equations of mixed type and their applications in transonic gas dynamics. It consists of Introduction, five Chapters and Appendix. In the Introduction a brief historical review and the structure of the book are given. In Chapter 1 the author analyses the behavior of characteristic curves on the plane for the cases which were not included in Cibrario's theory. The analysis uses classical methods of the qualitative theory of ordinary differential equations. In Chapter 2, which is central in the book, nonclassical equations of mixed type with smooth coefficients are treated. The equations are called nonclassical if they are irreducible by the transformation of variables to well-known equations having a single type degeneracy line that is not tangent to the characteristic direction at any point or, on the contrary, is a particular characteristic. The solvability of boundary value problems for wide classes of those equations in Sobolev spaces is studied. In Chapter 3 similar problems for model equations are considered. In Chapters 4 and 5 gasdynamical problems such as a flow in a Laval nozzle, nonisentropic flows and acoustic fields in nonuniform flows are treated. In the Appendix numerical results for acoustic vibrations in a Laval nozzle, disturbances in flows with perforated boundaries and a model jet radiation are presented.
scientific article; zbMATH DE number 108438