On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition
We identify the blow-up set of solutions to the problem 𝑢𝑡=(|𝑢𝑥|𝑝−2𝑢𝑥)𝑥, 𝑥>0, 𝑡∈(0,𝑇), −|𝑢𝑥|𝑝−2𝑢𝑥(0,𝑡)=𝑢𝑝−1(0,𝑡), 𝑡∈(0,𝑇), and 𝑢(𝑥,0)=𝑢0(𝑥)≥0, 𝑥>0, where 𝑝>2. We obtain that the blow up set 𝐵(𝑢) satisfies [0,𝑝(𝑝−1)/(𝑝−2))⊂𝐵(𝑢)⊂[0,𝑝(𝑝−1)/(𝑝−2)]. The proof is based on the analysis of the a...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/680572 |
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| author | Zhilei Liang |
| author_facet | Zhilei Liang |
| author_sort | Zhilei Liang |
| collection | DOAJ |
| description | We identify the blow-up set of solutions to the problem 𝑢𝑡=(|𝑢𝑥|𝑝−2𝑢𝑥)𝑥, 𝑥>0, 𝑡∈(0,𝑇), −|𝑢𝑥|𝑝−2𝑢𝑥(0,𝑡)=𝑢𝑝−1(0,𝑡), 𝑡∈(0,𝑇), and 𝑢(𝑥,0)=𝑢0(𝑥)≥0, 𝑥>0, where 𝑝>2. We obtain that the blow up set 𝐵(𝑢) satisfies [0,𝑝(𝑝−1)/(𝑝−2))⊂𝐵(𝑢)⊂[0,𝑝(𝑝−1)/(𝑝−2)]. The proof is based on the analysis of the asymptotic behavior of self-similar representation and on the comparison methods. |
| format | Article |
| id | doaj-art-c948266c99c047c6aff53d4b34ecb067 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c948266c99c047c6aff53d4b34ecb0672025-08-20T03:23:58ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/680572680572On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary ConditionZhilei Liang0School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaWe identify the blow-up set of solutions to the problem 𝑢𝑡=(|𝑢𝑥|𝑝−2𝑢𝑥)𝑥, 𝑥>0, 𝑡∈(0,𝑇), −|𝑢𝑥|𝑝−2𝑢𝑥(0,𝑡)=𝑢𝑝−1(0,𝑡), 𝑡∈(0,𝑇), and 𝑢(𝑥,0)=𝑢0(𝑥)≥0, 𝑥>0, where 𝑝>2. We obtain that the blow up set 𝐵(𝑢) satisfies [0,𝑝(𝑝−1)/(𝑝−2))⊂𝐵(𝑢)⊂[0,𝑝(𝑝−1)/(𝑝−2)]. The proof is based on the analysis of the asymptotic behavior of self-similar representation and on the comparison methods.http://dx.doi.org/10.1155/2010/680572 |
| spellingShingle | Zhilei Liang On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition Abstract and Applied Analysis |
| title | On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition |
| title_full | On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition |
| title_fullStr | On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition |
| title_full_unstemmed | On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition |
| title_short | On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition |
| title_sort | on the blow up set for non newtonian equation with a nonlinear boundary condition |
| url | http://dx.doi.org/10.1155/2010/680572 |
| work_keys_str_mv | AT zhileiliang ontheblowupsetfornonnewtonianequationwithanonlinearboundarycondition |