124,708 research outputs found
Degenerate integrodifferential equations of Volterra type in Banach space
No full textIl contributo è un articolo scientifico originale, non pubblicato altrove in nessuna forma.
Introduction: "This paper is concerned with the following degenerate integro-differential equation of parabolic type: \gathered \frac{d}{dt}(M(t)u(t))+L(t)u(t)+\int_0^t K(t,s)u(s)ds=f(t),\\0\leq t\leq T, M(t)u(t)|_{t=0}=M(0)u_0.\endgathered\tag1 This type of equation without the integral terms is discussed in great detail in Chapters III and IV of the book \ref[A. Favini and A. Yagi, Degenerate differential equations in Banach spaces, Dekker, New York, 1999; MR1654663 (99i:34079)] based on the theory of analytic semigroups generated by multi-valued linear operators. In Section 1, making intensive use of the results of [op. cit. (Chapter IV)], we show the existence and uniqueness of a solution to the non-autonomous equation (1) described above. We use the idea of M. G. Crandall and J. A. Nohel \ref[Israel J. Math. 29 (1978), no. 4, 313--328; MR0477910 (57 \#17410) (Proposition 1)] to deal with the integral term. Section 2 is devoted to the autonomous case based on the results of Chapter III of [A. Favini and A. Yagi, op. cit.]. In the non-autonomous case rather restrictive assumptions are required for certain constants which appear in the hypothesis for the operators and . In the autonomous case this restriction is considerably relaxed. Finally in Section 3 we consider the case in which the assumption (P) of [A. Favini and A. Yagi, op. cit. (p. 92)] is satisfied with . In this case using the method of J. Prüss \ref[J. Integral Equations 5 (1983), no. 3, 211--236; MR0702432 (85d:45026)], we show the existence and uniqueness of a function satisfying the integro-differential equation (1) with the integral term understood in the improper sense under a weaker assumption on the initial data.
Degenerate integrodifferential equations of parabolic type
No full textIl contributo è un articolo scientifico originale, non pubblicato altrove in nessuna forma, e sottoposto a referee. Il volume contiene solo articoli originali.We consider the initial value problem for a possibly degenerate in-tegrodifferential equation in L2(Ω) (eqution found) where M(t) = M0M1(t) is the multiplication operator by the function m(x, t) = m0(x)m1(x, t), m0(x) ≥ 0, m1(x, t) ≥ c > 0, L(t) is the realization in L2(Ω) of a second-order strongly elliptic operator in divergence form with Dirichlet or Neumann boundary conditions for all t, and B(t, s) is a linear differential operator of order ≤ 2 for each (t, s), 0 ≤ s ≤ t ≤ T, Ω being a bounded open set in Rn with a smooth boundary. We also establish a corresponding result in Lp(Ω), 1 < p < 3/2, related to Dirichlet boundary condition, only
Pressure Oscillations Numerical Simulation In Solid Rocket Motors
No full textLarge solid rocket motors can be affected by sustained pressure and thrust oscillations during the quasi-steady state. The root cause of this phenomenon is represented by the coupling between the vortices generation, shedding, advection and interaction with the SRM chamber geometry and the acoustic chamber modes excitement, which may act together, in a feedback coupled loop. In the present work, a Q1D model for the simulation of the pressure oscillations in solid rocket motors, named AGAR (Aerodynamically Generated Acoustic Resonance), is described, discussing a new formulation of the Q1D vorticity equation and of the closure terms for modeling the vortex sound generation. The results of the pressure oscillations simulation yielded with the new model formulation are discussed for the P80 solid rocket motor, first stage of the European launcher VEGA. © 2012 by E. Cavallini, V. Ferretti, B. Favini, M. Di Giacinto, F. Serraglia
Analysis of VEGA solid stages static firing tests towards the maiden flight
No full textVEGA is the new launcher developed by the European Space Agency and qualified with its maiden flight on February, 13rd 2012. During the launcher development, a total of eight static firing tests have been performed for the three solid stages (VEGA family SRMs), which compose the launcher: the first stage P80, the second stage Zefiro 23 and the third stage Z9A. In this work, the analysis of the static firing tests of the VEGA SRMs is performed with a post-static firing test reconstruction model, developed for the purpose. The aim is to use the measures acquired during the SFTs, in order to evaluate the actual behavior of the SRMs, through the parameters: combustion efficiency, thrust efficiency, hump, scale factor and nozzle throat area law, which define the actual performance parameters of the SRMs. The final purpose is to assess the SRMs performance parameters from the SFT data; to investigate the actual internal ballistics of the SRMs, comparing the outcomes of the SFT analysis, for each stage and, all together, all the VEGA family SRMs, in order to make possible the extrapolation of the flight conditions and to analyze the VEGA maiden flight. © 2012 by E. Cavallini, B. Favini, M. Di Giacinto, F. Serraglia
A two-step godunov-type scheme for the euler equations
No full textA second-order Godunov-type scheme for the Euler equations in conservation form is derived. The method is based on the ENO formulation proposed by Harten et al. The fundamental difference lies in the use of a two-step scheme to compute the time evolution. The scheme is TVD in the linear scalar case, and gives oscillation-free solutions when dealing with nonlinear hyperbolic systems. The admissible time step is twice that of classical Godunovtype schemes. This feature makes it computationally cheaper than one-step schemes, while requiring the same computer storage. © 1991 Kluwer Academic Publishers
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Convergence of two numerical schemes for turbulent boundary layer computations
No full textThe accuracy of numerical solutions for the incompressible turbulent boundary layer past a flat plate is addressed by means of a priori and a posteriori analysis. The former is carried out by computing the exact solutions of the Reynolds averaged Navier-Stokes equations with the Baldwin-Lomax and Spalart-Allmaras models; these solutions are used for the truncation error estimate in the modified equations. The latter is performed by applying a generalized Richardson extrapolation to the numerical solutions computed by two different finite volume techniques, namely a centered scheme with artificial dissipation and a ENO-type scheme. The results of the a priori theoretical analysis were confirmed by a posteriori analysis of numerical solutions
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