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A New Critical Phenomenon for Semilinear Parabolic Problems

โœ Scribed by Qi S. Zhang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
176 KB
Volume
219
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

We study the Cauchy problem of the inhomogeneous semilinear parabolic equations u + u p -u t + w = 0 on M n ร— 0 โˆž with initial value u 0 โ‰ฅ 0, where M n is a Riemannian manifold with possibly nonnegative Ricci curvature. There is an exponent p * which is critical in the following sense. When 1 < p โ‰ค p * , the above problem has no global positive solution for any nonnegative w = w x not identically zero and for any u 0 โ‰ฅ 0; when p > p * the problem has a global positive solution for some w = w x > 0 and some u 0 โ‰ฅ 0.

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