Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory
The author considers the nonlocal semilinear parabolic equation \[ u_t-\Delta u =\int_0^t u^p(x,t)\,ds, \quad x\in \Omega, t>0, \] under homogeneous Dirichlet boundary condition. For solutions that are monotone in time the blow-up rate is known to be the same as for the ODE \(u_t=u^p\). The author proves the existence of the monotone solutions.
scientific article; zbMATH DE number 2101585