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The absence of global positive solutions to semilinear parabolic differential inequalities in exterior domain


Author: Yuhua Sun
Journal: Proc. Amer. Math. Soc. 145 (2017), 3455-3464
MSC (2010): Primary 35K51; Secondary 35R45
DOI: https://doi.org/10.1090/proc/13472
Published electronically: January 26, 2017
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Abstract: We are concerned with the absence of global positive solutions to certain semi-linear parabolic differential inequalities in exterior domains with nontrivial boundary condition. Assuming that the boundary value is positive, we determine the critical value of the exponent of a nonlinear term, which is responsible for the nonexistence of a solution. In the case of vanishing boundary value, the critical exponent was previously found by G. Laptev (2003) and has a smaller value.


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Additional Information

Yuhua Sun
Affiliation: School of Mathematical Sciences and LPMC, Nankai University, 300071 Tianjin, People’s Republic of China
Email: sunyuhua@nankai.edu.cn

DOI: https://doi.org/10.1090/proc/13472
Keywords: Differential inequalities, critical exponent, exterior domain
Received by editor(s): March 15, 2016
Received by editor(s) in revised form: September 10, 2016
Published electronically: January 26, 2017
Communicated by: Joachim Krieger
Article copyright: © Copyright 2017 American Mathematical Society