IJPAM: Volume 116, No. 3 (2017)

Title

ESTIMATES OF LIFE SPAN OF
SOLUTIONS OF A CAUCHY PROBLEM

Authors

Joon Hyuk Kang
Department of Mathematics
Andrews University
Berrien Springs, MI, 49104, USA

Abstract

In this paper we get estimates of life span of a Cauchy problem

\begin{displaymath}\left.\begin{array}{rl}
u_{t}(x,t) = \Delta u(x,t) + u(x,t)^{...
...0,\\
u(x,0) = \lambda\phi(x), & x \in R^{n}
\end{array}\right.\end{displaymath}

in terms of the positive constant parameter $\lambda$ when $\phi(x)
\in L^{q}$ is a nonnegative bounded continuous function in $R^{n}$ but not identically zero, where $q$ is large enough. The technique we used in this paper is the Comparison Principle.

History

Received: 2017-04-05
Revised: 2017-09-13
Published: October 25, 2017

AMS Classification, Key Words

AMS Subject Classification:
Key Words and Phrases:

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Bibliography

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How to Cite?

DOI: 10.12732/ijpam.v116i3.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 3
Pages: 637 - 641


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