Difference analogues of orthogonal decompositions, basic differential operators and some boundary problems of mathematical physics. I

1964 ◽  
Vol 4 (3) ◽  
pp. 69-92 ◽  
Author(s):  
V.I. Lebedev
Keyword(s):  
Differential Operators ◽  
Mathematical Physics ◽  
Boundary Problems ◽  
Orthogonal Decompositions

scholarly journals Mathematical Modelling of Aquatic Ecosystem

2015 ◽  
Vol 3 ◽  
pp. 92
Author(s):  
Sharif E. Guseynov ◽  
Jekaterina V. Aleksejeva
Keyword(s):  
Mathematical Modelling ◽  
Mathematical Models ◽  
Aquatic Ecosystem ◽  
Initial Boundary ◽  
Mathematical Physics ◽  
Evolutionary Models ◽  
Dynamic Parameters ◽  
Aqueous Systems ◽  
Boundary Problems ◽  
Qualitative Models

<p class="R-AbstractKeywords"><span lang="EN-US">In present paper we consider the complete statements of initial-boundary problems for the modelling of various aspects of aqueous systems in Latvia. All the proposed models are the evolutionary models: all they are nonstationary and continuous qualitative models having the dynamic parameters and aimed at analysis, evaluation and forecast of aqueous systems (reservoirs, lakes and seas). In constructing these mathematical models as research tools classic apparatus of differential equations (both ODE and PDE) as well as apparatus of mathematical physics were used</span><span lang="EN-US">. </span></p>

scholarly journals RENORMALIZATION GROUP SYMMETRY AND SOPHUS LIE GROUP ANALYSIS

1995 ◽  
Vol 06 (04) ◽  
pp. 503-512 ◽  
Author(s):  
DMITRIJ V. SHIRKOV
Keyword(s):  
Lie Group ◽  
Group Analysis ◽  
Mathematical Physics ◽  
The Self ◽  
Group Symmetry ◽  
Lie Group Analysis ◽  
Short Discussion ◽  
Self Similarity ◽  
Boundary Problems ◽  
Solution Property

We start with a short discussion of the content of a term Renormalisation Group in modern use. By treating the underlying solution property as a reparametrisation symmetry, we relate it with the self-similarity symmetry well-known in mathematical physics and explain the notion of Functional Self-similarity. Then we formulate a program of constructing a regular approach for discovering RG-type symmetries in different problems of mathematical physics. This approach based upon S. Lie group analysis allows one to analyse a wide class of boundary problems for different type of equations. Several examples are mentioned.

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