On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes
Abstract
We study the Cauchy problem for a degenerate parabolic equation with source and inhomogeneous density of the form ut=div(ρ(x)um−1|Du|λ−1Du)+up in the case where initial function decreases slowly to zero as |x|→∞. We establish conditions for the existence and nonexistence of a global-in-time solution, which substantially depend on the behavior of the initial data as |x|→∞. In the case of global solvability, we obtain an exact estimate of a solution for large times.Downloads
Published
25.11.2012
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Section
Research articles
How to Cite
Martynenko, A. V., et al. “On the Behavior of Solutions of the Cauchy Problem for a Degenerate Parabolic Equation With Source in the Case Where the Initial Function Slowly Vanishes”. Ukrains’kyi Matematychnyi Zhurnal, vol. 64, no. 11, Nov. 2012, pp. 1500-15, https://umj.imath.kiev.ua/index.php/umj/article/view/2676.