Blow-Up for Quasilinear Heat Equations Described by Means of Nonlinear Hamilton–Jacobi Equations

AbstractIt is well-known that the nonnegative solutions of the semilinear heat equation[formula]blow up in a finite timeT(depending on the initial data, assumed to be large enough). This equation is interesting because it exhibits in differentβ-ranges the three most typical blow-up behaviours for solutions of nonlinear parabolic equations. Indeed, we consider radialy symmetric solutions and show that forβ>2 single-point blow-up occurs, forβ