Abstract
We consider the fractional in time Sobolev-type equation
partial derivative x(partial derivative(alpha)(0|t)u)=|u|(p), u(0,x) = u(0)(x), t > 0, x is an element of R,
where p > 1, 0<alpha<1 and partial derivative(alpha)(0|t) is the Caputo fractional derivative (with respect to time t) of order alpha. Using the nonlinear capacity method, we obtain a class of initial data u0 for which there are no local in time weak solutions; ie, we have an "instantaneous blow-up" of weak solutions.