Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group Analysis
Population balance equations may be employed to handle a wide variety of particle processes has certainly received unprecedented attention, but the absence of explicit exact solutions necessitates the use of numerical approaches. In this paper, a (2 + 1) dimensional population balance equation with...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/16/1/65 |
| _version_ | 1797342553911066624 |
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| author | Fubiao Lin Yang Yang Xinxia Yang |
| author_facet | Fubiao Lin Yang Yang Xinxia Yang |
| author_sort | Fubiao Lin |
| collection | DOAJ |
| description | Population balance equations may be employed to handle a wide variety of particle processes has certainly received unprecedented attention, but the absence of explicit exact solutions necessitates the use of numerical approaches. In this paper, a (2 + 1) dimensional population balance equation with aggregation, nucleation, growth and breakage processes is solved analytically by use of the methods of scaling transformation group, observation and trial function. Symmetries, reduced equations, invariant solutions, exact solutions, existence of solutions, evolution analysis of dynamic behavior for solutions are presented. The exact solutions obtained can be compared with the numerical scheme. The obtained results also show that the method of scaling transformation group can be applied to study integro-partial differential equations. |
| first_indexed | 2024-03-08T10:34:58Z |
| format | Article |
| id | doaj.art-f492afb479174a48aa1e98a8905597b7 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-08T10:34:58Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f492afb479174a48aa1e98a8905597b72024-01-26T18:38:47ZengMDPI AGSymmetry2073-89942024-01-011616510.3390/sym16010065Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group AnalysisFubiao Lin0Yang Yang1Xinxia Yang2School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaPopulation balance equations may be employed to handle a wide variety of particle processes has certainly received unprecedented attention, but the absence of explicit exact solutions necessitates the use of numerical approaches. In this paper, a (2 + 1) dimensional population balance equation with aggregation, nucleation, growth and breakage processes is solved analytically by use of the methods of scaling transformation group, observation and trial function. Symmetries, reduced equations, invariant solutions, exact solutions, existence of solutions, evolution analysis of dynamic behavior for solutions are presented. The exact solutions obtained can be compared with the numerical scheme. The obtained results also show that the method of scaling transformation group can be applied to study integro-partial differential equations.https://www.mdpi.com/2073-8994/16/1/65integro-partial differential equationpopulation balance equationscaling groupexact solution |
| spellingShingle | Fubiao Lin Yang Yang Xinxia Yang Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group Analysis Symmetry integro-partial differential equation population balance equation scaling group exact solution |
| title | Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group Analysis |
| title_full | Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group Analysis |
| title_fullStr | Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group Analysis |
| title_full_unstemmed | Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group Analysis |
| title_short | Exact Solutions of Population Balance Equation with Aggregation, Nucleation, Growth and Breakage Processes, Using Scaling Group Analysis |
| title_sort | exact solutions of population balance equation with aggregation nucleation growth and breakage processes using scaling group analysis |
| topic | integro-partial differential equation population balance equation scaling group exact solution |
| url | https://www.mdpi.com/2073-8994/16/1/65 |
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