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Subsolutions and super solutions to systems of parabolic equations with applications to generalized Fujita-type systems

✍ Scribed by G. Lu; B. D. Sleeman

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
514 KB
Volume
17
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

A constructive method for obtaining subsolutions and supersolutions to the Cauchy problem for systems of parabolic equations is discussed. Applications of the method to Fujita‐type systems are considered leading to global existence and finite time blow‐up results.

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Finding the general solution of a singular system of linear equations requires computing a particular solution and a basis of the null space of the corresponding singular matrix. In this paper, we consider the case where the singular matrix is large and sparse, and the application calls for a direct