Premium
Singular curve and critical curve for doubly nonlinear Lane–Emden type equations
Author(s) -
Huang Haochuan,
Huang Rui,
Yin Jingxue
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7408
Subject(s) - mathematics , domain (mathematical analysis) , nonlinear system , mathematical analysis , regular polygon , type (biology) , sequence (biology) , work (physics) , geometry , ecology , physics , quantum mechanics , biology , mechanical engineering , genetics , engineering
This paper is concerned with singular curve and critical curve for the periodic doubly nonlinear Lane–Emden type equation∂ u ∂ t − div ( | ∇ u m| p − 2 ∇ u m ) = a ( x , t ) u q . In 2010, under a convex assumption on the domain Ω, Wang et al. (2010) considered a partial case of p − 1 < q m < p − 1 + p − 1 m N . While, there are no results about the cases ofq m ≤ p − 1 andq m ≥ p − 1 + p − 1 m Nbefore the present work. In this paper, we fill the gap for these two cases and give a total classification for the exponents. Furthermore, by constructing a special blow‐up sequence, we remove the convex assumption on the domain Ω, not only for the partial case considered in Wang et al. (2010) but also for other remaining cases.