Gevrey regularity of the solutions of some inhomogeneous semilinear partial differential equations with variable coefficients

Pascal Remy ()
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Pascal Remy: Université de Versailles Saint-Quentin

Partial Differential Equations and Applications, 2023, vol. 4, issue 3, 1-18

Abstract: Abstract In this article, we are interested in the Gevrey properties of the formal power series solution in time of some partial differential equations with a power-law nonlinearity and with analytic coefficients at the origin of $${\mathbb {C}}^2$$ C 2 . We prove in particular that the inhomogeneity of the equation and the formal solution are together s-Gevrey for any $$s\geqslant s_c$$ s ⩾ s c , where $$s_c$$ s c is a nonnegative rational number fully determined by the Newton polygon of the associated linear PDE. In the opposite case $$s

Keywords: Gevrey order; Inhomogeneous partial differential equation; Nonlinear partial differential equation; Newton polygon; Formal power series; Divergent power series; 35C10; 35C20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-023-00236-0

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