Ill-posedness of nonlinear parabolic equation with critical initial condition

Abstract: We study the initial boundary value problem of strongly nonlinear parabolic equation:@[email protected][email protected][email protected][email protected]?x"[email protected][email protected]?x"i^p^-^[email protected][email protected]?x"i+u^1^+^@awith critical initial data. By introducing a family of potential wells the global nonexistence of solution is proved, which solves the open problem existing in some classical literature.