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Supersolutions for parabolic equations with unbounded or degenerate diffusion coefficients and their applications to some classes of parabolic and hyperbolic equations

Supersolutions for parabolic equations with unbounded or degenerate diffusion coefficients and their applications to some classes of parabolic and hyperbolic equations

This paper is concerned with supersolutions to parabolic equations of the form \begin{equation} \partial_t U (x,t)-D(x)ΔU(x,t)=0, \quad (x,t)\in \mathbb{R}^N \times (0,\infty), \end{equation} where $D\in C(\mathbb{R}^N)$ is positive. Under the behavior of the diffusion coefficient $D$ with polynomial order at spatial infinity, a family of supersolutions with slowly decaying property at …