Muratbekov, Madi
[Author]
;
H. Begehr
[Contributor];
K. Ospanov
[Contributor]
Approximate properties of solutions and spectrum character of some classes of mixed type equations ; Approximative Eigenschaften von Lösungen und Spektralcharakter einiger Klassen gemischter Gleichungen
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Media type:
Doctoral Thesis;
E-Book;
Electronic Thesis
Title:
Approximate properties of solutions and spectrum character of some classes of mixed type equations ; Approximative Eigenschaften von Lösungen und Spektralcharakter einiger Klassen gemischter Gleichungen
Contributor:
Muratbekov, Madi
[Author]
imprint:
Freie Universität Berlin: Refubium (FU Berlin), 2008
Footnote:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Description:
Title Page and table of contents Introduction 2 1\. Coercitive estimates and estimates of the spectrum of mixed type operators 16 1.1 Estimates of the spectrum for a class of mixed type equation 21 1.2 Estimates of the spectrum of a class of mixed type equation with coefficients of two variables 31 1.3 Properties of the resolvent and estimates of eigenvalues for a mixed type operator 42 2\. Solvability and smoothness of solutions of the semiperiodical Dirichlet problem for mixed type equations 56 2.1 Separability of a mixed type operator 56 2.2 Two-sides estimates of the distribution function of s-values of \ a class of mixed type differential operators 68 Literature 101 Zusammenfassung ; The thesis is devoted to the investigation of spectral properties of the semiperiodical Dirichlet problem for mixed type equations depending on the behavior of the coefficients in bounded and unbounded domains. The conditions on the coefficients of the lower order terms of a mixed type operator have some influence on the existence of the resolvent and the separability of a mixed type operator. The following new results are obtained: boundedness and compactness of the resolvent of a mixed type operator corresponding to the semiperiodical Dirichlet problem for mixed type equations; two-sided estimates of Schmidt eigenvalues (s-values) and estimates of eigenvalues of the resolvent; coercitive solvability of the semiperiodical Dirichlet problem for a class of mixed type equations; it is proved that the conditions of boundedness from below for the coefficients of the lowest term is significant for the separability of a mixed type operator in an unbounded domain; solvability of the semiperiodical Dirichlet problem for a class of mixed type equations with fast-growing coefficients in an unbounded domain and smoothness of solutions; conditions providing discreteness of the spectrum for a class of the mixed type equations with fast-growing coefficients; asymptotic of s-values and their distribution function for a class of mixed type ...