Fujita exponent on stratified Lie groups

Durvudkhan Suragan; Bharat Talwar

doi:10.1007/s13348-023-00427-3

Fujita exponent on stratified Lie groups

Durvudkhan Suragan, Bharat Talwar

School of Sciences and Humanities

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that QQ-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.

Original language	English
Journal	Collectanea Mathematica
DOIs	https://doi.org/10.1007/s13348-023-00427-3
Publication status	Accepted/In press - 2023

Keywords

Dilations
Fujita exponent
Global solution
Stratified Lie group
Subelliptic operator

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s13348-023-00427-3

Cite this

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title = "Fujita exponent on stratified Lie groups",

abstract = "We prove that QQ-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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author = "Durvudkhan Suragan and Bharat Talwar",

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AU - Talwar, Bharat

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AB - We prove that QQ-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.

KW - Dilations

KW - Fujita exponent

KW - Global solution

KW - Stratified Lie group

KW - Subelliptic operator

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Fujita exponent on stratified Lie groups

Abstract

Keywords

ASJC Scopus subject areas

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