Existence and asymptotic behavior of solutions to a quasi-linear hyperbolic-parabolic model of vasculogenesis
We consider a hyperbolic-parabolic model of vasculogenesis in the multidimensional case. For this system we show the global existence of smooth solutions to the Cauchy problem, using suitable energy estimates. Since this model does not enter in the classical framework of dissipative problems, we ana...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
April 4, 2013
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| In: |
SIAM journal on mathematical analysis
Year: 2013, Jahrgang: 45, Heft: 2, Pages: 748-776 |
| ISSN: | 1095-7154 |
| DOI: | 10.1137/110858896 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/110858896 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/110858896 
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| Verfasserangaben: | Cristiana Di Russo and Alice Sepe |
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| 520 | |a We consider a hyperbolic-parabolic model of vasculogenesis in the multidimensional case. For this system we show the global existence of smooth solutions to the Cauchy problem, using suitable energy estimates. Since this model does not enter in the classical framework of dissipative problems, we analyze it combining the features of the hyperbolic and the parabolic parts. Moreover we study the asymptotic behavior of those solutions showing their decay rates by means of detailed analysis of the Green function for the linearized problem. | ||
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