Hadamard's fundamental solution and multiple-characteristic problems.
Heat distribution in a medium with concentrated perturbation of density.
Heat kernels for class 2 nilpotent groups
Heat polynomial analogs for higher order evolution equations.
Heaviside's theory of signal transmission on submarine cables
As written in L. Schwartz' book, Heaviside's theory of cables is an important source of the theory of generalized functions. The partial differential equations he discussed were the usual heat equation and the simplest hyperbolic equations of one space dimension, but he had to solve them as evolution equations in the unusual direction of the distance along which the electric signals propagate. Although he obtained explicit expressions of solutions, which were of great economical values, it has not...
High order transmission conditions for thin conductive sheets in magneto-quasistatics
We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...
High order transmission conditions for thin conductive sheets in magneto-quasistatics
We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...
Higher-order KdV-type equations and their stability.
Hilbert space valued generalized random processes. II.
Homogénéisation d'équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux
Homogenization of a boundary condition for the heat equation
An asymptotic analysis is given for the heat equation with mixed boundary conditions rapidly oscillating between Dirichlet and Neumann type. We try to present a general framework where deterministic homogenization methods can be applied to calculate the second term in the asymptotic expansion with respect to the small parameter characterizing the oscillations.
Homogenization of a non-linear quasi-stationary Maxwell problem