Abstract
This article presents necessary conditions for the existence of weak solutions of the following space-nonlocal evolution equations on H x (0, +infinity), where H is the Heisenberg group:
partial derivative(2)u/partial derivative t(2) + (-Delta H)(alpha/2)vertical bar u vertical bar(m) = vertical bar u vertical bar(p),
partial derivative u/partial derivative t + (-Delta(H))(alpha/2)vertical bar u vertical bar(m) = vertical bar u vertical bar(p),
partial derivative(2)u/partial derivative t(2) + (-Delta H)(alpha/2)vertical bar u vertical bar(m) + partial derivative u/partial derivative t = vertical bar u vertical bar(p),
p is an element of R, p > 1, m is an element of N. Moreover, the life span for each equation is estimated under some suitable conditions. Our method of proof is based on the test function method.