On the uniqueness of initial-value problems for partial differential equations of the first order
We consider viscosity solutions for first order differential-functional equations. Uniqueness theorems for initial, mixed, and boundary value problems are presented. Our theorems include some results for generalized ("almost everywhere") solutions.
We discuss the uniqueness of solutions to problems like⎧ λ |u|s-1u - div (|∇u|p-2∇u) = μ on Ω,⎨⎩ u = 0 in ∂Ω,where λ ≥ 0 and μ is a signed Radon measure.
We consider the initial-boundary value problem for first order differential-functional equations. We present the `vanishing viscosity' method in order to obtain viscosity solutions. Our formulation includes problems with a retarded and deviated argument and differential-integral equations.
We study the flow of a compressible, stationary and irrotational fluid with wake, in a channel, around a convex symmetric profile, with assigned velocity q-infinity at infinity and q-s < q-infinity at the wake. In particular, we study the regularity of the free boundary (for a problem which has non-constant coefficients), in the hodograph plane.
Two problems arising in Environment are considered. The first one concerns a conjecture posed by von Neumann in 1955 on the possible modification of the albedo in order to control the Earth surface temperature. The second one is related to the approximate controllability of Stackelberg-Nash strategies for some optimization problems as, for instance, the pollution control in a lake. The results of the second part were obtained in collaboration with Jacques-Lois Lions.
Si considerano problemi di controllo ottimale con una dipendenza non lineare tra il controllo e lo stato. Si mostra come in certi casi la continuità di tale dipendenza, quindi la buona posizione nel senso di Tychonov, è connessa alla forma del funzionale costo. In particolare si esamina un problema di Stefan a due fasi con controllo distribuito nel termine di sorgente.
The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.
FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model...
Viscous two-fluid flows arise in different kinds of coating technologies. Frequently, the corresponding mathematical models represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In this review article we present some results about nonisothermal stationary as well as about isothermal evolutionary viscous flow problems. The temperature-depending problems are characterized by coupled heat- and mass transfer and also by thermocapillary convection....
A mathematical model of heat and mass transport in non-isothermal partially saturated oil-wax solution was formulated by A. Fasano and M. Primicerio [1]. This paper is devoted to the study of a one-dimensional problem in the framework of that model. The existence of classical solutions in a small time interval is proved, based on the application of a fixed-point theorem to the constructed operator. The technique employed is close to the one of [3] and [4].