ABSTRACT

From a unique viewpoint, singular elliptic and parabolic second-order inequalities with quasilinear KPZ-type terms are investigated in cylindrical domains. The weight Neumann condition is set on the lateral area of the cylinder; no condition is set on the base of the cylinder (regardless the type of the equation). Results of two kinds are established: the existence of a limit of each solution (if it exists) along the axis of the cylinder and sufficient conditions of a blow-up (including instant or complete one).

中文翻译：

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具有 KPZ 非线性的奇异方程的具有加权 Neumann 条件的非经典平稳和非平稳问题

摘要

从独特的角度，研究了圆柱域中具有拟线性 KPZ 类型项的奇异椭圆和抛物线二阶不等式。在圆柱的侧面积上设置权重诺依曼条件；没有在圆柱体的基础上设置条件（无论方程的类型如何）。建立了两种结果：沿圆柱轴的每个解的极限（如果存在）和爆破的充分条件（包括瞬间或完全爆破）。