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Heat kernel

In the mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate boundary conditions. It is also one of the main tools in the study of the spectrum of the Laplace operator, and is thus of some auxiliary importance throughout mathematical physics. The heat…

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Definition

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Heat kernel

Nodes34
Edges33
Triples32
Avg. degree1.94
Density0.058824
Components1

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Heat kernel

Top relations

related to Definition · 15
Heat kernel → Bessel, Delta, Dirac, Euclidean, Gaussian, Here, Jacobi, More, Nevertheless, Omega, On, Rd, Riemannian, The, This
related to Spectral theory · 11
Heat kernel → Delta, Dirichlet, Dirichlet Laplacian, Formally, However, L2, Laplacian, Let, Omega, The, To
is a · 3
Heat kernel → fundamental solution to the heat equation on a specified domain with appropriate boundary conditions, heat kernel of d-dimensional Euclidean space Rd, solution of the initial boundary value problem
see also · 3
Heat kernel → Generalizations, Heat, Pleijel

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Important terminology

heat kernel displaystyle boundary delta also mathematical function lim phi equation domain study smooth spectral rd frac begin partial end

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Heat kernelis afundamental solution to the heat equation on a specified domain with appropriate boundary conditions0.90text
Heat kernelis aheat kernel of d-dimensional Euclidean space Rd0.90text
Heat kernelis asolution of the initial boundary value problem0.90text
Heat kernelrelated to DefinitionThe0.60section
Heat kernelrelated to DefinitionEuclidean0.60section
Heat kernelrelated to DefinitionRd0.60section
Heat kernelrelated to DefinitionGaussian0.60section
Heat kernelrelated to DefinitionThis0.60section
Heat kernelrelated to DefinitionDelta0.60section
Heat kernelrelated to DefinitionHere0.60section
Heat kernelrelated to DefinitionDirac0.60section
Heat kernelrelated to DefinitionOn0.60section

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