The authors consider the initial value problem \(u_t= \alpha(u)_{xx}\), \(u(0, x)= u_0(x)\), where \(\alpha(u)= u^n\) if \(u\geq 0\) and \(|u|^{m- 1} u\) if \(u\leq 0\) with \(0< n\leq 1< m\), \(u_0\in L^1(\mathbb{R})\). Under additional assumptions on supports of positive and negative parts of the initial function they prove that the solution \(u(t, x)\) of the problem is positive if and only if \(x< a(t)\), where \(a(t)\) is determined via the negative part of the solution. Also, it is proved that \(u(t, x)\) becomes positive on \(x\in \mathbb{R}\) for sufficiently large \(t\) provided that \(\int_{\mathbb{R}} u_0(x) dx> 0\).