@article{953e1051ac224b78aaea09fc7faf52fb,
title = "The Cauchy problem for heat equations with exponential nonlinearity",
abstract = "The Cauchy problem for the semilinear heat equations is studied in the Orlicz space exp L 2(R{double-struck}n), where any power behavior of interaction works as a subcritical nonlinearity. We prove the existence of global solutions for the semilinear heat equations with the exponential nonlinearity under the smallness condition on the initial data in exp L2(R{double-struck}n).",
keywords = "Cauchy problems, Critical Sobolev embeddings, Global existence, Orlicz spaces",
author = "Norisuke Ioku",
note = "Funding Information: The author would like to express his gratitude to Professor Takayoshi Ogawa for valuable advice and continuous encouragement. He also expresses his sincere thanks to Professor Michinori Ishiwata for his helpful comment. He is grateful to the referees for their helpful comments on the paper. This work was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.",
year = "2011",
month = aug,
day = "15",
doi = "10.1016/j.jde.2011.02.015",
language = "English",
volume = "251",
pages = "1172--1194",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "4-5",
}