Theory of spaces with dominating mixed derivative

1982 ◽  
Vol 31 (5) ◽  
pp. 345-354
Author(s):  
Yu. A. Brychkov
Keyword(s):  
Mixed Derivative

scholarly journals Non-local problem with integral conditions for the three-dimensional high order hyperbolic equations

2020 ◽  
pp. 51-62
Author(s):  
Ш.Ш. Юсубов
Keyword(s):  
Integral Equation ◽  
Hyperbolic Equation ◽  
Hyperbolic Equations ◽  
Three Dimensional ◽  
High Order ◽  
Mixed Derivative ◽  
Local Problem ◽  
Integral Conditions ◽  
Order Hyperbolic Equation ◽  
Non Local

В работе для трехмерного гиперболического уравнения высокого порядка с доминирующей смешанной производной исследуется разрешимость нелокальной задачи с интегральными условиями. Поставленная задача сводится к интегральному уравнению и с помощью априорных оценок доказывается существование единственного решения. In the work the solvability of the non-local problem with integral conditions is investigated for the three-dimensional high order hyperbolic equation with dominated mixed derivative. The problem is reduced to the integral equation and existence of the solution is proved by the help of aprior estimations.

Use of a mixed derivative for the gas chromatography and mass spectrometry of cytidine and its analogs

1977 ◽  
Vol 82 (1) ◽  
pp. 217-225 ◽  
Author(s):  
U.I. Krahmer ◽  
J.G. Liehr ◽  
K.J. Lyman ◽  
E.A. Orr ◽  
R.N. Stillwell ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Gas Chromatography ◽  
Mixed Derivative

scholarly journals Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zulfiqar Ali ◽  
Syed Husnine ◽  
Imran Naeem
Keyword(s):  
Exact Solutions ◽  
Fourth Order ◽  
Arbitrary Function ◽  
Mixed Derivative ◽  
Reduction Theory ◽  
Double Reduction ◽  
Derivative Term ◽  
Divergence Property

We find exact solutions of the Generalized Modified Boussinesq (GMB) equation, the Kuromoto-Sivashinsky (KS) equation the and, Camassa-Holm (CH) equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.

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