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arXiv · 2510.20702

The Cauchy problem for $p$-evolution equations with initial data in Gelfand-Shilov spaces

Marco Cappiello·Eliakim Cleyton Machado
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Abstract

We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$ large, we prove a well-posedness result in Gelfand-Shilov spaces.

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Marco Cappiello, Eliakim Cleyton Machado. 2025-10-23. The Cauchy problem for $p$-evolution equations with initial data in Gelfand-Shilov spaces. https://arxiv.org/abs/2510.20702

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