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Some Sharp Estimates for Parabolic Equations

โœ Scribed by Alain Haraux

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
275 KB
Volume
187
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

Sharp estimates are given for the constants appearing in both the smoothing effect of general self-adjoint contraction semi-groups and uniform estimates for the linear heat equation. The last estimate is used to prove rather sharp global existence results for some nonlinear perturbations and suitable initial data in a quite simple and convenient way.

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## Abstract We study the Cauchy problem for the quasilinear parabolic equation magnified image where __p__ > 1 is a parameter and ฯˆ is a smooth, bounded function on (1, โˆž) with โˆ’ โฉฝ __s__ฯˆโ€ฒ(__s__)/ฯˆ(__s__) โฉฝ ฮธ for some ฮธ > 0. If 1 < __p__ < 1 + 2/__N__, there are no global positive solutions, wherea