Li, Jun-jie; Zhang, Jing-jun Instantaneous shrinking of the support for solutions of parabolic variational inequalities. (Chinese. English summary) Zbl 1084.35038 Appl. Math., Ser. A (Chin. Ed.) 20, No. 3, 303-312 (2005). Summary: The paper considers the following parabolic variational inequalities: \[ \forall v\geq 0,\;\bigl(u_t-\Delta u+b(x,t)u^p\bigr)(v-u)\geq f(v-u)\text{ a.e., }(x,t) \in\mathbb{R}^N\times(0,T], \]\[ u\geq 0,\;(x,t)\in\mathbb{R}^N\times (0,T], \]\[ u(x,0)=u_0 (x),\;x\in\mathbb{R}^N, \] Some qualitative properties for solutions of these variational inequalities, such as existence, uniqueness and instantaneous shrinking of the support, are studied here. MSC: 35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs Keywords:existence; uniqueness PDFBibTeX XMLCite \textit{J.-j. Li} and \textit{J.-j. Zhang}, Appl. Math., Ser. A (Chin. Ed.) 20, No. 3, 303--312 (2005; Zbl 1084.35038)