Concerning an equation in the theory of combustion
The author is concerned with the following Cauchy problem for a classical equation involved in the theory of combustion \[ \begin{cases} \frac{\partial\theta}{\partial t}=\frac{1}{\delta}\Delta\theta+e^\theta &\text{in } \mathbb{R}^+\times\mathbb{R}^N\\ \theta_{| t=0}=\theta_0(x) &\text{in } \mathbb{R}^N, \end{cases} \] where \(\theta\) is the temperature of the medium and \(\delta\) is a positive parameter. The initial condition \(\theta_0\) is \(L^1_{loc}(\mathbb{R},\mathbb{R}^+)\). The author proves nonexistence of solution for \(t\geq T^*\) and then blow up of the solution at \(T_*\), for some \(T_*\). The method of nonlinear capacity is used.
scientific article; zbMATH DE number 5980649
scientific article