Impulsive effects on global existence of solutions for degenerate semilinear parabolic equations
The paper deals with quenching and blow-up of solutions of initial-boundary value problem for impulsive degenerate semilinear parabolic equations \[ \Biggl(x^q{\partial\over \partial t}-{\partial^2\over\partial x^2}\Biggr) u=\lambda f(u),\quad x\in(0,1),\quad (n-1)\;T< t\leq nT^-, \] \[ u(x,0)= u_0(x),\quad u(x, nT)= \sigma u(x, nT^-),\quad x\in[0, 1],\quad u(0,t)= 0= u(1,t),\quad t>0. \] The authors prove that for \(\sigma< 1\) there exists a unique critical length and study the decay of the solutions. For \(\sigma> 1\), it is proved that there exists a unique critical length, and three criteria for blow-up of solutions are obtained.
scientific article; zbMATH DE number 1183225