Journal
INDIANA UNIVERSITY MATHEMATICS JOURNAL
Volume 69, Issue 6, Pages 2171-2207Publisher
INDIANA UNIV MATH JOURNAL
DOI: 10.1512/iumj.2020.69.7989
Keywords
Critical Fujita exponent; blow-up; global solution; Schrodinger operator
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Funding
- Japan Society for the Promotion of Science
- [15H02058]
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We study the existence/nonexistence of global-in-time positive solutions of the Cauchy problem (P) {partial derivative(t)u = Delta u - V(x)u + u(p), x is an element of R-N, t > 0, u(x,0) = phi(x) >= 0, x is an element of R-,(N) where p > 1 and V is a radially symmetric function decaying quadratically at the space infinity. We identify the so-called critical Fujita exponent for problem (P).
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