The Method of Layer Potentials for the Heat Equation in Lipschitz Cylinders

1989/04/01 by Russell M. Brown, R. M. Brown · 13 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods

paper · doi:10.2307/2374513

Abstract

Pour l'equation de la chaleur dans des cylindres de Lipschitz on etudie des problemes aux valeurs limites d'initiales avec conditions de Neumann et de Dirichlet

Cited by

• L 2 Solvability and Representation by Caloric Layer Potentials in Time- Varying Domains
• A relation between the Dirichlet and the Regularity problem for parabolic equations
• A Liouville theorem for stationary and ergodic ensembles of parabolic\n systems
• Quantitative Estimates in Homogenization of Parabolic Systems of Elasticity in Lipschitz Cylinders
• The L^p regularity problem for parabolic operators with transversally independent coefficients
• Boundary integral operator for the fractional Laplace equation in a bounded Lipschitz domain
• An adaptive fast Gauss transform in two dimensions
• A fast Gauss transform in one dimension using sum-of-exponentials approximations
• Shape sensitivity analysis of the heat equation and the Dirichlet-to-Neumann map
• Boundary behaviour of layer potentials for the multi-term time-fractional diffusion equation
• On Initial-Boundary Value Problem of Stochastic Heat Equation in a Lipschitz Cylinder
• The Dirichlet boundary problem for second order parabolic operators satisfying Carleson condition
• On the Regularity Problem for Parabolic Operators and the Role of Half-Time Derivative. [europepmc]

Related

• Full Asymptotics and Laurent Series of Layer Potentials for Laplace's\n Equation on the Half-Space
• The L^p Boundary Value Problems on Lipschitz Domains
• Newtonian and single layer potentials for the Stokes system with L^∞ coefficients and the exterior Dirichlet problem
• Variational views of stokeslets and stresslets
• Dependence of the layer heat potentials upon support perturbations