Galaktionov, V. A.; Posashkov, S. A. Application of new comparison theorem in the investigation of unbounded solutions of nonlinear parabolic equations. (English. Russian original) Zbl 0632.35028 Differ. Equations 22, 809-815 (1986); translation from Differ. Uravn. 22, No. 7, 1165-1173 (1986). Working on the example of the Cauchy problem for the semilinear parabolic equation \[ u_ t=u_{xx}+u^{\beta},\quad t>0,\quad x\in R^ 1;\quad u(0,x)=u_ 0(x)>0,\quad x\in R^ 1,\quad \beta =const>1, \] some new applications of the strong maximum principle are given to investigate the unbounded positive solutions \(u(t,x)>0\), existing only on a finite time interval. Reviewer: I.Ginchev Cited in 1 ReviewCited in 18 Documents MSC: 35K55 Nonlinear parabolic equations 35B50 Maximum principles in context of PDEs 35K15 Initial value problems for second-order parabolic equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:Cauchy problem; semilinear; strong maximum principle; unbounded positive solutions; finite time interval PDFBibTeX XMLCite \textit{V. A. Galaktionov} and \textit{S. A. Posashkov}, Differ. Equations 22, 809--815 (1986; Zbl 0632.35028); translation from Differ. Uravn. 22, No. 7, 1165--1173 (1986)