Critical non-linearity for some evolution equations with Fujita-type
critical exponent
Critical non-linearity for some evolution equations with Fujita-type
critical exponent
We consider the Cauchy problem for a class of non-linear evolution equations in the form \[L(\partial_t,\partial_x) u=F(\partial_t^\ell u), \quad (t,x)\in [0,\infty)\times \mathbb{R}^n;\] here, $L(\partial_t,\partial_x)$ is a linear partial differential operator with constant coefficients, of order $m\geq 1$ with respect to the time variable $t$, and $\ell$ is a natural number …