Nonexistence results for a higher-order evolution equation with an inhomogeneous term depending on time and space

Abstract

We consider a higher-order evolution equation with an inhomogeneous term depending on time and space. We first derive a general criterion for the nonexistence of weak solutions. Next, we study the particular case when the inhomogeneity depends only on space. In that case, we obtain the first critical exponent in the sense of Fujita, as well as the second critical exponent in the sense of Lee and Ni.