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arXiv · 2211.10759

Fujita exponent on stratified Lie groups

Durvudkhan Suragan·Bharat Talwar
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Abstract

We prove that $\frac{Q}{Q-2}$ is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension $Q$. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon a group element and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem.

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Durvudkhan Suragan, Bharat Talwar. 2022-11-19. Fujita exponent on stratified Lie groups. https://doi.org/10.1007/s13348-023-00427-3

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