Nonexistence of nonnegative solutions for parabolic inequalities in the half-space

Abstract

Based on the method of nonlinear capacity, we study the nonexistence of nonnegative monotonic solutions for the quasilinear parabolic inequality $u_t-\Delta_p u\ge u^q$. Also we study generalizations in the half-space in terms of parameters p and q.

Keywords

• Quasilinear parabolic inequalities
• monotonicity
• nonexistence of solutions