The Cauchy problem for ut = Δu(m) when 0<m<1
| dc.contributor.author | Herrero, Miguel A. | |
| dc.contributor.author | Pierre, Michel | |
| dc.date.accessioned | 2023-06-21T02:03:14Z | |
| dc.date.available | 2023-06-21T02:03:14Z | |
| dc.date.issued | 1985-09 | |
| dc.description.abstract | This paper deals with the Cauchy problem for the nonlinear diffusion equation ∂u/∂t - Δ (u|u|m+1) = 0 on (0, ∞) x RN,u(0, .) = u0 when 0 < m < 1 (fast diffusion case). We prove that there exists a global time solution for any locally integrable function u0: hence, no growth condition at infinity for u0 is required. Moreover the solution is shown to be unique in that class. Behavior at infinity of the solution and L∞loc-regularizing effects are also examined when m Є (max{(N-2)/N, 0}, 1). | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17623 | |
| dc.identifier.doi | 10.2307/1999900 | |
| dc.identifier.issn | 0002-9947 | |
| dc.identifier.officialurl | http://www.ams.org/journals/tran/1985-291-01/S0002-9947-1985-0797051-0/S0002-9947-1985-0797051-0.pdf | |
| dc.identifier.relatedurl | http://www.ams.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64723 | |
| dc.issue.number | 1 | |
| dc.journal.title | Transactions of the American Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 158 | |
| dc.page.initial | 145 | |
| dc.publisher | American Mathematical Society | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.955 | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Cauchy problem | |
| dc.subject.keyword | nonlinear diffusion | |
| dc.subject.keyword | initial-value problem | |
| dc.subject.keyword | regularizing effects. | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | The Cauchy problem for ut = Δu(m) when 0<m<1 | |
| dc.type | journal article | |
| dc.volume.number | 291 | |
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| dspace.entity.type | Publication |
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