We study the large-time behavior of the sublinear viscosity solution to a singular Hamilton–Jacobi equation that appears in a critical coagulation-fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our results include complete characterizations of stationary solutions and optimal conditions to guarantee large-time convergence. In particular, we obtain convergence results under certain natural conditions on the initial data, and a nonconvergence result when such conditions fail.

中文翻译：

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临界凝聚-破碎模型中Hamilton-Jacobi方程的长时间行为

我们研究了一个奇异的Hamilton-Jacobi方程的亚线性粘度解的长时间行为，该方程出现在具有混凝作用和恒定碎裂核的临界混凝-破碎模型中。我们的结果包括固定解的完整表征和确保长时间收敛的最佳条件。特别是，我们在某些自然条件下获得了初始数据的收敛结果，而当这些条件失败时将获得非收敛结果。