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Some results on a singular parabolic equation in one dimension case
Author(s) -
Zhou Wenshu,
Wei Xiaodan
Publication year - 2013
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.2778
Subject(s) - uniqueness , mathematics , dimension (graph theory) , constant (computer programming) , novelty , mathematical analysis , parabolic partial differential equation , pure mathematics , partial differential equation , philosophy , theology , computer science , programming language
This paper is concerned with the existence, nonexistence, uniqueness, and non‐uniqueness of solutions for a singular parabolic equation in one dimension case. For different cases of some constant m of the equation, we study the uniqueness of solutions for m > − 1, the nonexistence of solutions for m ≤ − p , and the existence and non‐uniqueness of solutions for − p < m ≤ − 1. The novelty of this paper lies in the study of nonexistence. Moreover, the other results of this paper extend some recent works. Copyright © 2013 John Wiley & Sons, Ltd.