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This article is cited in 14 scientific papers (total in 14 papers)
Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems
S. E. Pastukhova
Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
Abstract:
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.
DOI:
https://doi.org/10.4213/sm3793
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English version:
Sbornik: Mathematics, 2007, 198:10, 1465–1494
Bibliographic databases:
    
UDC:
517.956.226+517.956.8+517.957.95
MSC: 35J60, 47J05
Received: 31.10.2006 and 02.04.2007
Citation:
S. E. Pastukhova, “Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems”, Mat. Sb., 198:10 (2007), 89–118; Sb. Math., 198:10 (2007), 1465–1494
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