We study the homogenization of parabolic or hyperbolic equations likewhen the coefficients , (defined in ) take possibly high values on a -periodic set of grain-like inclusions of vanishing measure. Memory effects arise in the limit problem.
We study the homogenization of parabolic or hyperbolic equations like when the coefficients , (defined in Ω) take possibly high values on a ε-periodic set of grain-like inclusions of vanishing measure. Memory effects arise in the limit problem.
We take some well-known inequalities for Green functions relative to Laplace’s equation, and prove not only analogues of them relative to the heat equation, but generalizations of those analogues to the heat potentials of nonnegative measures on an arbitrary open set whose supports are compact polar subsets of . We then use the special case where the measure associated to the potential has point support, in the following situation. Given a nonnegative supertemperature on an open set , we prove...
In this talk we shall present some joint work with A. Grigory’an. Upper and lower estimates on the rate of decay of the heat kernel on a complete non-compact riemannian manifold have recently been obtained in terms of the geometry at infinity of the manifold, more precisely in terms of a kind of isoperimetric profile. The main point is to connect the decay of the norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods. We shall...