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Instantaneous shrinking of the support for solutions of parabolic variational inequalities. (Chinese. English summary) Zbl 1084.35038

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
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