Gevrey index theorem for the inhomogeneous n-dimensional heat equation with a power-law nonlinearity and variable coefficients
We are interested in the Gevrey properties of the formal power series solution in time of the inhomogeneous semilinear heat equation with a powerlaw nonlinearity in 1-dimensional time variable t ∈ C and n-dimensional spatial variable x ∈ C n and with analytic initial condition and analytic coefficie...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
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| Sorozat: | Acta scientiarum mathematicarum
87 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-020-571-9 |
| Online Access: | http://acta.bibl.u-szeged.hu/73921 |
| LEADER | 01409nab a2200205 i 4500 | ||
|---|---|---|---|
| 001 | acta73921 | ||
| 005 | 20211115155601.0 | ||
| 008 | 211115s2021 hu o 0|| eng d | ||
| 022 | |a 2064-8316 | ||
| 024 | 7 | |a 10.14232/actasm-020-571-9 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Remy Pascal | |
| 245 | 1 | 0 | |a Gevrey index theorem for the inhomogeneous n-dimensional heat equation with a power-law nonlinearity and variable coefficients |h [elektronikus dokumentum] / |c Remy Pascal |
| 260 | |c 2021 | ||
| 300 | |a 163-181 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 87 No. 1-2 | |
| 520 | 3 | |a We are interested in the Gevrey properties of the formal power series solution in time of the inhomogeneous semilinear heat equation with a powerlaw nonlinearity in 1-dimensional time variable t ∈ C and n-dimensional spatial variable x ∈ C n and with analytic initial condition and analytic coefficients at the origin x = 0. We prove in particular that the inhomogeneity of the equation and the formal solution are together s-Gevrey for any s ≥ 1. In the opposite case s < 1, we show that the solution is generically 1-Gevrey while the inhomogeneity is s-Gevrey, and we give an explicit example in which the solution is s -Gevrey for no s ′ < 1. | |
| 695 | |a Matematika | ||
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/73921/1/math_087_numb_001-002_163-181.pdf |z Dokumentum-elérés |