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 |
Tartalmi kivonat: | 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. |
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Terjedelem/Fizikai jellemzők: | 163-181 |
ISSN: | 2064-8316 |