Blow-up of solutions of semilinear hyperbolic equations in one space dimension
The paper deals with the Cauchy problem NEWLINE\[NEWLINE\partial^2_t u-\partial^2_x u=G(u,u_x,u_t),\;x\in\mathbb{R},\;t>0,NEWLINE\]NEWLINE NEWLINE\[NEWLINE\partial^j_t u=\psi_j,\;x\in \mathbb{R},\;t=0,\;j=0,1,NEWLINE\]NEWLINE where \(G\in C^1(\mathbb{R}^3)\), \(\psi_j\in C^{2-j} (\mathbb{R})\), \(j=0,1\). The author discusses results on the maximal influence domain of solutions of the above Cauchy problem and related mixed problems.
scientific article; zbMATH DE number 1672555