Conditions aux limites approchées pour les couches minces périodiques
Conditions aux limites approchées pour les couches minces périodiques
Nous écrivons et nous justifions des conditions aux limites approchées pour des couches minces périodiques recouvrant un objet parfaitement conducteur en polarisation transverse électrique et transverse magnétique.
Constructing soliton and kink solutions of PDE models in transport and biology.
Construction de paramétrixes pour des opérateurs pseudodifférentiels caractéristiques sur la réunion de deux cônes lissés
Construction de solutions pour les équations de Korteweg-de Vries généralisées
Construction de solutions singulières pour des équations aux dérivées partielles non linéaires
Construction du noyau de Bergman local
Construction of Singular Solutions to the P-Harmonic Equation and its Limit Equation for P = ... .
Construction solutions of PDE in parametric form.
Contributo allo studio dei fenomeni di trasporto della carica minoritaria in regioni quasi neutre di semiconduttori fortemente e disuniformemente drogati. Riduzione del problema ad equazioni integrali
Transport phenomena of minority carriers in quasi neutral regions of heavily doped semiconductors are considered for the case of one-dimensional stationary flow and their study is reduced to a Fredholm integral equation of the second kind, the kernel and the known term of which are built from known functions of the doping arbitrarily distributed in space. The advantage of the method consists, among other things, in having all the coefficients of the differential equations and of the boundary conditions...
Control of Traveling Solutions in a Loop-Reactor
We consider the stabilization of a rotating temperature pulse traveling in a continuous asymptotic model of many connected chemical reactors organized in a loop with continuously switching the feed point synchronously with the motion of the pulse solution. We use the switch velocity as control parameter and design it to follow the pulse: the switch velocity is updated at every step on-line using the discrepancy between the temperature at the front...
Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension
We study controllability for a nonhomogeneous string and ring under an axial stretching tension that varies with time. We consider the boundary control for a string and distributed control for a ring. For a string, we are looking for a control f(t) ∈ L2(0, T) that drives the state solution to rest. We show that for a ring, two forces are required to achieve controllability. The controllability problem is reduced to a moment problem...
Convergence of formal solutions of first order singular nonlinear partial differential equations in the complex domain
We study the convergence or divergence of formal (power series) solutions of first order nonlinear partial differential equations (SE) f(x,u,Dx u) = 0 with u(0)=0. Here the function f(x,u,ξ) is defined and holomorphic in a neighbourhood of a point and . The equation (SE) is said to be singular if f(0,0,ξ) ≡ 0 . The criterion of convergence of a formal solution of (SE) is given by a generalized form of the Poincaré condition which depends on each formal solution. In the case where the formal...
Convergence of iterative methods applied to generalized Fisher equation.
Convergence of power series along vector fields and their commutators; a Cartan-Kähler type theorem
We study convergence of formal power series along families of formal or analytic vector fields. One of our results says that if a formal power series converges along a family of vector fields, then it also converges along their commutators. Using this theorem and a result of T. Morimoto, we prove analyticity of formal solutions for a class of nonlinear singular PDEs. In the proofs we use results from control theory.
Convergence, via summability, of formal power series solutions to a certain class of completely integrable Pfaffian systems
Cooling of a layered plate under mixed conditions.
Cooling of a plate with general boundary conditions.
Couches limites de systèmes paraboliques
Covariant differential operators and Green's functions
The basic idea of this paper is to use the covariance of a partial differential operator under a suitable group action to determine suitable associated Green’s functions. For instance, we offer a new proof of a formula for Green’s function of the mth power of the ordinary Laplace’s operator Δ in the unit disk found in a recent paper (Hayman-Korenblum, J. Anal. Math. 60 (1993), 113-133). We also study Green’s functions associated with mth powers of the Poincaré invariant Laplace operator . It turns...