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 the group elements 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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Acknowledgements
The authors are grateful to the anonymous referee for pointing out an error and suggesting an alternate solution.
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This research was funded by Nazarbayev University under grants 20122022CRP1601 and 20122022FD4105.
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Suragan, D., Talwar, B. Fujita exponent on stratified Lie groups. Collect. Math. (2023). https://doi.org/10.1007/s13348-023-00427-3
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DOI: https://doi.org/10.1007/s13348-023-00427-3