Nonexistence of Global Weak Solutions for Evolution Equations with Fractional Laplacian

Abstract: A nonlocal nonlinear parabolic equation with fractional Laplacian is considered. By means of the method of test functions, the nonexistence of nontrivial global weak solutions is demonstrated. Simultaneously, the nonexistence of nontrivial weak solutions for the corresponding elliptic case is established. © 2020, Pleiades Publishing, Ltd.