TY - JOUR
T1 - Existence and nonexistence of solutions for the heat equation with a superlinear source term
AU - Fujishima, Yohei
AU - Ioku, Norisuke
N1 - Funding Information:
The authors would like to express their sincere thanks to the reviewer for his/her informative suggestions. The nonexistence result (Theorem 1.2) and its proof are refined by the suggestions. This work was partially funded by JSPS KAKENHI (grant number 15K17573 and 15K17575) and Sumitomo Fundation (grant number 140825).
Funding Information:
The authors would like to express their sincere thanks to the reviewer for his/her informative suggestions. The nonexistence result ( Theorem 1.2 ) and its proof are refined by the suggestions. This work was partially funded by JSPS KAKENHI (grant number 15K17573 and 15K17575 ) and Sumitomo Fundation (grant number 140825 ).
Publisher Copyright:
© 2018 Elsevier Masson SAS
PY - 2018/10
Y1 - 2018/10
N2 - We develop a classification theory for the existence and non-existence of local in time solutions for initial value problems for nonlinear heat equations. By focusing on some quasi-scaling property and its invariant integral, we reveal the explicit threshold integrability of initial data that classifies the existence and nonexistence of solutions. Typical nonlinear terms, for instance polynomial type, exponential type and their sums, products and compositions can be treated as applications.
AB - We develop a classification theory for the existence and non-existence of local in time solutions for initial value problems for nonlinear heat equations. By focusing on some quasi-scaling property and its invariant integral, we reveal the explicit threshold integrability of initial data that classifies the existence and nonexistence of solutions. Typical nonlinear terms, for instance polynomial type, exponential type and their sums, products and compositions can be treated as applications.
KW - Existence and nonexistence
KW - Nonlinear heat equation
KW - Scale invariance
KW - Singular initial data
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U2 - 10.1016/j.matpur.2018.08.001
DO - 10.1016/j.matpur.2018.08.001
M3 - Article
AN - SCOPUS:85051402255
VL - 118
SP - 128
EP - 158
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
SN - 0021-7824
ER -