On the Heisenberg group, the semilinear damped wave equation with |u|^p has Fujita critical exponent p_Fuj(Q)=1+2/Q: global small-data solutions for p above it, blow-up for p at or below it.
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Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity
On the Heisenberg group, the semilinear damped wave equation with |u|^p has Fujita critical exponent p_Fuj(Q)=1+2/Q: global small-data solutions for p above it, blow-up for p at or below it.