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

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  • Pascal Remy

    (Université de Versailles Saint-Quentin)

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

Suggested Citation

  • Pascal Remy, 2023. "Gevrey regularity of the solutions of some inhomogeneous semilinear partial differential equations with variable coefficients," Partial Differential Equations and Applications, Springer, vol. 4(3), pages 1-18, June.
    • Handle: RePEc:spr:pardea:v:4:y:2023:i:3:d:10.1007_s42985-023-00236-0
    DOI: 10.1007/s42985-023-00236-0
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