The heat equation and harmonic maps of complete manifolds.
The heat equation and the shrinking.
The heat equation in riemannian geometry
The heat flows and harmonic maps of complete noncompact Riemannian manifolds.
The heat kernel on Lie groups.
The heat transform and its use in thermal identification problems for electronic circuits.
The initial value problem for parabolic equations with data in
The initial-boundary value problem for some pseudoparabolic system in unbounded domain.
The interior regularity and the Liouville property for the quasilinear parabolic systems
The Kolmogorov equation with time-measurable coefficients.
The Neumann problem for the heat equation in non-cylindrical domains
I shall discuss joint work with John L. Lewis on the solvability of boundary value problems for the heat equation in non-cylindrical (i.e., time-varying) domains, whose boundaries are in some sense minimally smooth in both space and time. The emphasis will be on the Neumann problem with data in . A somewhat surprising feature of our results is that, in contrast to the cylindrical case, the optimal results hold when , with the situation getting progressively worse as approaches . In particular,...
The solvability of the Dirichlet problems for parabolic equations
For two general second order parabolic equations in divergence form in Lip(1,1/2) cylinders, we give a criterion for the preservation of solvability of the Dirichlet problems.
The linear-quadratic optimal control problem for delay differential equations
In questo lavoro si considera il problema del controllo ottimo per un'equazione lineare con ritardo in uno spazio di Hilbert, con costo quadratico. Si dimostra che il problema della sintesi si traduce in una equazione di Riccati in uno opportuno spazio prodotto e si prova che tale equazione ammette un’unica soluzione.
The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition
We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition with a locally defined, -bounded function . We prove the existence of a local weak solution to the problem by means of the Rothe method. A uniform a priori estimate for the Rothe approximations in , which is required by the local assumptions on , is derived by...
The logarithmic delay of KPP fronts in a periodic medium
We extend, to parabolic equations of the KPP type in periodic media, a result of Bramson which asserts that, in the case of a spatially homogeneous reaction rate, the time lag between the position of an initially compactly supported solution and that of a traveling wave grows logarithmically in time.
The logarithmic gradient of the kernel of the heat equation with drift on a Riemannian manifold.
The maximum principle for equations with composite coefficients.
The Method of Lines for Nonlinear Parabolic Differential Equations with Mixed Derivatives.
The method of normal splines for linear implicit differential equations of second order.
The method of Rothe and two-scale convergence in nonlinear problems
Modelling of macroscopic behaviour of materials, consisting of several layers or components, cannot avoid their microstructural properties. This article demonstrates how the method of Rothe, described in the book of K. Rektorys The Method of Discretization in Time, together with the two-scale homogenization technique can be applied to the existence and convergence analysis of some strongly nonlinear time-dependent problems of this type.