A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat Equation
Fixed and moving boundary problems for the one-dimensional heat equation are considered. A unified approach to solving such problems is proposed by embedding a given initial-boundary value problem into an appropriate initial value problem on the real line with arbitrary but given functions, whose so...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/7/749 |
| _version_ | 1827696267650662400 |
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| author | Marianito R. Rodrigo Ngamta Thamwattana |
| author_facet | Marianito R. Rodrigo Ngamta Thamwattana |
| author_sort | Marianito R. Rodrigo |
| collection | DOAJ |
| description | Fixed and moving boundary problems for the one-dimensional heat equation are considered. A unified approach to solving such problems is proposed by embedding a given initial-boundary value problem into an appropriate initial value problem on the real line with arbitrary but given functions, whose solution is known. These arbitrary functions are determined by imposing that the solution of the initial value problem satisfies the given boundary conditions. Exact analytical solutions of some moving boundary problems that have not been previously obtained are provided. Moreover, examples of fixed boundary problems over semi-infinite and bounded intervals are given, thus providing an alternative approach to the usual methods of solution. |
| first_indexed | 2024-03-10T12:44:17Z |
| format | Article |
| id | doaj.art-39ab83cf985142e3ac182e5701b1549e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:44:17Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-39ab83cf985142e3ac182e5701b1549e2023-11-21T13:35:47ZengMDPI AGMathematics2227-73902021-03-019774910.3390/math9070749A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat EquationMarianito R. Rodrigo0Ngamta Thamwattana1School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, AustraliaSchool of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, AustraliaFixed and moving boundary problems for the one-dimensional heat equation are considered. A unified approach to solving such problems is proposed by embedding a given initial-boundary value problem into an appropriate initial value problem on the real line with arbitrary but given functions, whose solution is known. These arbitrary functions are determined by imposing that the solution of the initial value problem satisfies the given boundary conditions. Exact analytical solutions of some moving boundary problems that have not been previously obtained are provided. Moreover, examples of fixed boundary problems over semi-infinite and bounded intervals are given, thus providing an alternative approach to the usual methods of solution.https://www.mdpi.com/2227-7390/9/7/749heat equationanalytical solutionmoving boundary problemfixed boundary problem |
| spellingShingle | Marianito R. Rodrigo Ngamta Thamwattana A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat Equation Mathematics heat equation analytical solution moving boundary problem fixed boundary problem |
| title | A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat Equation |
| title_full | A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat Equation |
| title_fullStr | A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat Equation |
| title_full_unstemmed | A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat Equation |
| title_short | A Unified Analytical Approach to Fixed and Moving Boundary Problems for the Heat Equation |
| title_sort | unified analytical approach to fixed and moving boundary problems for the heat equation |
| topic | heat equation analytical solution moving boundary problem fixed boundary problem |
| url | https://www.mdpi.com/2227-7390/9/7/749 |
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