Well-Posedness and Regularity of the Heat Equation with Robin Boundary Conditions in the Two-Dimensional Wedge

2024/11/07 by Marco Bravin, Bravin, Marco, Manuel V. Gnann +9 · 1 citation
Computer Science · Engineering · Mathematics · #35B34 #35J25 #35K05 #35K67 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2411.04651

openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Well-posedness and higher regularity of the heat equation with Robin boundary conditions in an unbounded two-dimensional wedge is established in an L²-setting of monomially weighted spaces. A mathematical framework is developed which allows to obtain arbitrarily high regularity without a smallness assumption on the opening angle of the wedge. The challenging aspect is that the resolvent problem exhibits two breakings of the scaling invariance, one in the equation and one in the boundary condition.

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