Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems
- Moscow State Institute of Radio Engineering, Electronics and Automatics (Technical University), Moscow (Russian Federation)
A non-linear monotone equation with degenerate weight function is considered. In the general case the smooth functions are not dense in the corresponding weighted Sobolev space W, which leads to a non-uniqueness of a particular kind. Taking for the energy space either W itself or its subspace H equal to the closure of the smooth functions one obtains at least two uniquely soluble problems. In addition, there exist infinitely many weak solutions distinct from the W- and H-solutions. The problem of approximability or attainability is considered: which solutions of the original equation can be obtained as limits of solutions of the equations with suitable non-degenerate weights? It is shown that the W- and the H-solutions are attainable; in both cases a regular approximation algorithm is described. Bibliography: 14 titles.
- OSTI ID:
- 21267088
- Journal Information:
- Sbornik. Mathematics, Vol. 198, Issue 10; Other Information: DOI: 10.1070/SM2007v198n10ABEH003892; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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