1,721,129 research outputs found
Local solvability for semilinear partial differential equations of constant strength
No full textThe main goal of the present paper is to study the local solvability of semilnear partial differential operators of the form F(u) = P(D)u + ∫(x, Q 1(D)u, ....... Q M(D)u). where P(D), Q 1(D), .... Q M(D) are linear partial differntial operators of constant coefficients and ∫(x, v) is a C ∞ function with respect to x and an entire function with respect to v. Under suitable assumptions on the nonlinear function ∫ and on P, Q 1, .... Q M, we will solve locally near every point x 0 ∈ R n the next equation F(u) = g, g ∈ B p,k. where B p,k is a wieghted Sobolev space as in Hörmander [13]
Projekta za Pulu – Progetti per Pola
No full textLa pubblicazione raccoglie i progetti didattici per aree della città di Pola interessate da presenze storico-archeologiche, sviluppati da docenti dello IUAV: G. Dubbini, F. Messina, G. Fraziano, S. Maffioletti, G. Malacarne, E. Mantese, P. Montini Zimolo, A. Rossi, A. Rudi, R. Sordina, V. Spigai. La pubblicazione è introdotta da Luciano Semerani
Local solvability for semilinear Fuchsian equations
No full textWe consider a semilinear elliptic operator P on a manifold B with a conical singular point. We assume P is Fuchs type in the linear part and has a non-linear lower order therms. Using the Schauder fixed point theorem, we prove the local solvability of P near the conical point in the weighted Sobolev spaces
Unique continuation and continuous dependence results for a severely ill-posed integro-differential parabolic problem
No full textVia Carleman estimates we determine sufficient conditions ensuring uniqueness and continuous dependence results for a severely ill-posed linear integro-differential boundary-value parabolic problem with no initial condition. This latter condition is replaced with an additional boundary information prescribing the temperature on an open subset of the geometric domai
Approximation of solutions to linear integro-differential parabolic equations in L^p-spaces
No full textIn this paper we show that, under suitable assumptions, the solutions to the approximating initial and boundary value problems (Pε) (cf. introduction) converge in Lp((0,T);Ls(Ω)), for suitable indexes p[1,+∞) and s[1,+∞), to the solution to the limit problem (P0). The last two Sections 4–5 are devoted to a similar approximation result, in a Banach-space framework, and involve a generalization of the kernels k, h and operator A
An identification problem with evolution on the boundary of parabolic type
No full textWe consider an equation of the type A(u + k * u) = f, where A is a linear second-order elliptic operator, k is a scalar function depending on time only and k * u denotes the standard time convolution of functions defined on R with their supports in [0, T]. The previous equation is endowed with dynamical boundary conditions. Assuming that the kernel k is unknown and information is given, under suitable additional conditions k can be recovered and global existence, uniqueness and continuous dependence results can be shown
Identification problems for Maxwell integro-differential equations related to media with cylindric symmetries
No full textAs is well known, the propagation of electromagnetic waves in dispersive media is governed by integro-differential equations. We assume here that the medium is a rigid body with a cylindric symmetry. In this case all the physical characteristics, such as the dielectric coefficient, the magnetic permeability and the conductivity coefficient as well as the kernels accounting for memory effects, may be assumed to depend only on the distance from the axis of the cylinder. Our aim is to solve the inverse problem, consisting in determining, in addition to the electromagnetic field, also the relaxation kernels, by the means of additional measurements. Existence, uniqueness and continuous dependence results are proved in the context of suitable functional spaces
Local solvability for nonlinear partial differential equations
No full textIn the introduction we give a short survey on known results concerning local solvability for nonlinear partial differential equations; the next sections will be then devoted to the proof of a new result in the same direction. Specifically we study the semi-linear operator F(u) = P(D)u + f(x, Q 1(D)u, .., Q M(D)u) where P, Q 1, .., Q M are linear partial differential operators with constant coefficients and f(x, v), x ∈ R n, v ∈ C M, is a smooth function with respect to x and entire with respect to v. Let g be in the Hörmander space B p,k we want to solve locally near a point x 0 ∈ R n the equation F(u) = g
An identification problem with evolution on the boundary of hyperbolic type
No full textWe consider an equation of the type , where is a linear second-order elliptic operator, is a scalar function depending on time only and denotes the standard time convolution of functions defined in with their supports in . The previous equation is endowed with dynamical boundary conditions.
\pn
Assuming that the kernel is unknown and a supplementary condition is given, can be recovered and global existence, uniqueness and continuous dependence results can be shown
Unique continuation and continuous dependence results for a severely ill-posed integrodifferential parabolic problem with a memory term in the principal part of the differential operator
No full textWe prove uniqueness and continuous dependence results for a severely ill-posed
linear integrodifferential boundary-value parabolic problem with no initial condition. This
latter condition is replaced with an additional boundary information prescribing the temperature
on an open subset of the geometric domain .
The integral operators entering the equation are defined by integrals of Volterra type
with respect to time. In particular, the class of integrodifferential equations dealt with
in this paper include those occurring in the linear theory of heat flow in a rigid body
consisting of a material with thermal memory
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