We investigate the problem of a high-energy source localized within a one-dimensional superdiffusive medium of finite length. The problem is modeled by a fractional diffusion equation with a nonlinear source term. For the boundary conditions, we consider both the case of homogeneous Dirichlet conditions and the case of homogeneous Neumann conditions. We investigate this model to determine whether or not blow-up occurs. It is demonstrated that a blow-up may or may not occur for the Dirichlet case. On the other hand, a blow-up is unavoidable for the Neumann case.
- fractional diffusion equation
- nonlinear Volterra integral equations
- thermal blow-up
ASJC Scopus subject areas
- Applied Mathematics