Nonlinear Parabolic Equation on Manifolds
- Gladson Antunes
- Ivo Lopez
- Maria Silva
- Luiz Medeiros
- Angela Biazutti
Abstract
In this work we investigate the existence and the uniqueness of solution for a nonlinear differential equation of parabolic type on the lateral boundary $\Sigma$ of a cylinder $Q$, cf. (1). An important part of our study is to transform this initial value problem into another one whose differential operator equation is of the type\[
u_{t}+a\left({\displaystyle\int_{\Gamma}}udx\right) \mathcal{A}%
u-\Delta_{\Gamma}u+u^{2k+1}=f \,\, \text{on} \,\, \Sigma,
\]
cf. (9), where $k$ is a positive integer. The operator $\mathcal{A}$ acts in Sobolev spaces on $\Gamma$, boundary of $\Omega$. The initial value problem (9) will be studied in Section $4$. Thus, we obtain the existence and the uniqueness of weak solution for (9).
- Full Text:
PDF
- DOI:10.5539/jmr.v6n1p85
Journal Metrics
- h-index (December 2021): 22
- i10-index (December 2021): 78
- h5-index (December 2021): N/A
- h5-median (December 2021): N/A
( The data was calculated based on Google Scholar Citations. Click Here to Learn More. )
Index
- Academic Journals Database
- ACNP
- Aerospace Database
- BASE (Bielefeld Academic Search Engine)
- Civil Engineering Abstracts
- CNKI Scholar
- COPAC
- DTU Library
- EconPapers
- Elektronische Zeitschriftenbibliothek (EZB)
- EuroPub Database
- Google Scholar
- Harvard Library
- IDEAS
- Infotrieve
- JournalTOCs
- LOCKSS
- MathGuide
- MathSciNet
- MIAR
- PKP Open Archives Harvester
- Publons
- RePEc
- ResearchGate
- Scilit
- SHERPA/RoMEO
- SocioRePEc
- Standard Periodical Directory
- Technische Informationsbibliothek (TIB)
- The Keepers Registry
- UCR Library
- Universe Digital Library
- WorldCat
Contact
- Sophia WangEditorial Assistant
- jmr@ccsenet.org