Well-posedness results and blow-up for a class of semilinear heat equations

Abstract

Abstract This paper considers the initial value problem for nonlinear heat equation in the whole space R N $\mathbb{R}^{N}$ . The local existence theory related to the finite time blow-up is also obtained for the problem with nonlinearity source (like polynomial types).

Keywords

• Nonlinear heat equation
• Existence
• Blow-up