A remark on the global solvability of the Cauchy problem for quasilinear parabolic equations
The present article is devoted to studying the global solvability of the Cauchy problem for the quasilinear parabolic equation NEWLINE\[NEWLINE\begin{gathered} u_t = a(t,x,u,u_x)u_{xx} + f(t,x,u,u_x)\quad\text{in } \Pi_T (0,T)\times \mathbb{R}, \\ u(x,0) = u_0(x)\quad\text{for } x\in \mathbb{R}. \end{gathered}NEWLINE\]NEWLINE The main aim of the article under review is to expose a new (weaker) sufficient condition which guarantees the global solvability of the Cauchy problem. The author investigates the case of the arbitrary order of growth of the function \(f(t,x,u,p)\) with respect to \(p\) when \(|p|\to\infty\).
scientific article; zbMATH DE number 1655650
scientific article