Heat equation and the principle of not feeling the boundary

DOI10.1017/S0308210500018722zbMath0687.35044OpenAlexW2319116696MaRDI QIDQ4205821

Michiel van den Berg

Publication date: 1989

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500018722

zbMATH Keywords

Dirichlet problemheat kernelsprinciple of not feeling the boundary

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Heat equation (35K05) Qualitative properties of solutions to partial differential equations (35B99)

Related Items (9)

Feeling boundary by Brownian motion in a ball ⋮ A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces ⋮ On the Placement of an Obstacle so as to Optimize the Dirichlet Heat Content ⋮ Solvability for time‐fractional semilinear parabolic equations with singular initial data ⋮ Strong space-time convexity and the heat equation ⋮ A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations ⋮ Laplace Dirichlet heat kernels in convex domains ⋮ Non-uniqueness for a critical heat equation in two dimensions with singular data ⋮ Extreme hitting probabilities for diffusion*

Cites Work

• Classical boundary conditions as a technical tool in modern mathematical physics
• On the asymptotics of the heat equation and bounds on traces associated with the Dirichlet Laplacian

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