Large time behavior of reaction–diffusion equations with Bessel generators

Abstract: We investigate explosion in finite time of one-dimensional semilinear equations of the form with initial value , where is positive and , are constants. In the free case we provide conditions on φ under which any positive nontrivial solution is non-global. In the case and , , which includes in the special case the equation we use the Feynman–Kac formula for Bessel processes to give conditions on the equation parameters ensuring finite-time blowup and existence of nontrivial positive global solutions. [Copyright &y& Elsevier]