Irregular linear systems of PDEs with the conditions on solutions' projections

Autor:	Sidorov, Nikolai A.
Rok vydání:	2018
Předmět:	Mathematics - Analysis of PDEs Mathematics - Functional Analysis 35L05
Druh dokumentu:	Working Paper
Popis:	The theory of complete generalized Jordan sets is employed to reduce the PDE with the irreversible linear operator $B$ of finite index to the regular problems. It is demonstrated how the question of the choice of boundary conditions is connected with the $B$-Jordan structure of coefficients of PDE. The various approaches shows the combination alternative Lyapunov method, Jordan structure coefficients and skeleton decomposition of irreversible linear operator from the main part equation are among the most powerfull methods to attack such challenging problem. On this base the complex problem of the {\it correct choice of boundary conditions} for the wide class of the singular PDE can be solved. Aggregated existence and uniqueness theorems can be proved, solution may continuously depend on the function determied from the experiments. Such theory can be applied to the integral--differential equations with partial derivatives.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1812.09694 Zobrazit plný text záznamu View this record from Arxiv