Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients View Full Text


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Article Info

DATE

2019-04

AUTHORS

Yohei Fujishima, Tatsuki Kawakami, Yannick Sire

ABSTRACT

We investigate a non-homogeneous semilinear heat equation which involves degenerate coefficients. More precisely, in order to give a rather complete theory, we focus on two types of weights w(x)=|x1|a or w(x)=|x|b where a,b>0 in a suitable range. We prove the existence of a Fujita exponent and describe the dichotomy existence/non-existence of global in time solutions. The coefficients under consideration admit either a singularity at the origin or a line of singularities. In this latter case, the problem is related to the fractional Laplacian, through the Caffarelli–Silvestre extension and is a first attempt to develop a parabolic theory in this setting. More... »

PAGES

62

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00526-019-1525-0

DOI

http://dx.doi.org/10.1007/s00526-019-1525-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112874583


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