The Existence of Entropy Solutions for a Class of Parabolic Equations
The existence and uniqueness of entropy solutions for a class of parabolic equations involving a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</...
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/17/3753 |
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| author | Zengfei Chen Bingliang Shen |
| author_facet | Zengfei Chen Bingliang Shen |
| author_sort | Zengfei Chen |
| collection | DOAJ |
| description | The existence and uniqueness of entropy solutions for a class of parabolic equations involving a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplace operator are investigated. We first prove existence of the global weak solution for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian equations with regular initial data via the difference and variation methods as well as the standard domain expansion technique. Then, by constructing and solving a related approximation problem, the entropy solution for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian equations with irregular initial data in whole space is also obtained. |
| first_indexed | 2024-03-10T23:17:04Z |
| format | Article |
| id | doaj.art-1a9e0acba7dd4df48faef08eddef80c4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:17:04Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1a9e0acba7dd4df48faef08eddef80c42023-11-19T08:31:40ZengMDPI AGMathematics2227-73902023-08-011117375310.3390/math11173753The Existence of Entropy Solutions for a Class of Parabolic EquationsZengfei Chen0Bingliang Shen1Zhejiang College, Shanghai University of Finance & Economics, Jinhua 321013, ChinaZhejiang College, Shanghai University of Finance & Economics, Jinhua 321013, ChinaThe existence and uniqueness of entropy solutions for a class of parabolic equations involving a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplace operator are investigated. We first prove existence of the global weak solution for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian equations with regular initial data via the difference and variation methods as well as the standard domain expansion technique. Then, by constructing and solving a related approximation problem, the entropy solution for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian equations with irregular initial data in whole space is also obtained.https://www.mdpi.com/2227-7390/11/17/3753variable exponententropy solutiontruncation functionvariational methods |
| spellingShingle | Zengfei Chen Bingliang Shen The Existence of Entropy Solutions for a Class of Parabolic Equations Mathematics variable exponent entropy solution truncation function variational methods |
| title | The Existence of Entropy Solutions for a Class of Parabolic Equations |
| title_full | The Existence of Entropy Solutions for a Class of Parabolic Equations |
| title_fullStr | The Existence of Entropy Solutions for a Class of Parabolic Equations |
| title_full_unstemmed | The Existence of Entropy Solutions for a Class of Parabolic Equations |
| title_short | The Existence of Entropy Solutions for a Class of Parabolic Equations |
| title_sort | existence of entropy solutions for a class of parabolic equations |
| topic | variable exponent entropy solution truncation function variational methods |
| url | https://www.mdpi.com/2227-7390/11/17/3753 |
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