DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS
DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS
DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS
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ON PARABOLIC SYSTEMS WITH DISCONTINUOUS<br />
NONLINEARITIES<br />
H. DEGUCHI<br />
We present existence, uniqueness, and stability results for the initial value problems for<br />
parabolic systems with discontinuous nonlinearities.<br />
Copyright © 2006 H. Deguchi. This is an open access article distributed under the Creative<br />
Commons Attribution License, which permits unrestricted use, distribution, and<br />
reproduction in any medium, provided the original work is properly cited.<br />
1. Introduction<br />
In this paper, we will study weak solutions of the initial value problem<br />
u t = u xx + f (u) − f (1)H(v − β), 0