On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation
By Oleinik's line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in [0,T]×R2: ∂xxu+u∂yu−∂tu=f(⋅,u), provided that T is suitable small. Results of numerical experiments are reported to demonstrate that the strong solu...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/827087 |
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| _version_ | 1849415482582499328 |
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| author | Zongqi Liang Huashui Zhan |
| author_facet | Zongqi Liang Huashui Zhan |
| author_sort | Zongqi Liang |
| collection | DOAJ |
| description | By Oleinik's line method, we study the existence and the uniqueness of the classical
solution of the Cauchy problem for the following equation in [0,T]×R2: ∂xxu+u∂yu−∂tu=f(⋅,u), provided that T is suitable small. Results of numerical experiments
are reported to demonstrate that the strong solutions of the above
equation may blow up in finite time. |
| format | Article |
| id | doaj-art-68c7a42c05834a5385b3f11204d8448f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-68c7a42c05834a5385b3f11204d8448f2025-08-20T03:33:31ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/827087827087On the Cauchy Problem of a Quasilinear Degenerate Parabolic EquationZongqi Liang0Huashui Zhan1School of Science, Jimei University, Xiamen 361021, ChinaSchool of Science, Jimei University, Xiamen 361021, ChinaBy Oleinik's line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in [0,T]×R2: ∂xxu+u∂yu−∂tu=f(⋅,u), provided that T is suitable small. Results of numerical experiments are reported to demonstrate that the strong solutions of the above equation may blow up in finite time.http://dx.doi.org/10.1155/2009/827087 |
| spellingShingle | Zongqi Liang Huashui Zhan On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation Discrete Dynamics in Nature and Society |
| title | On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation |
| title_full | On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation |
| title_fullStr | On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation |
| title_full_unstemmed | On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation |
| title_short | On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation |
| title_sort | on the cauchy problem of a quasilinear degenerate parabolic equation |
| url | http://dx.doi.org/10.1155/2009/827087 |
| work_keys_str_mv | AT zongqiliang onthecauchyproblemofaquasilineardegenerateparabolicequation AT huashuizhan onthecauchyproblemofaquasilineardegenerateparabolicequation |