1,134 research outputs found
Semilinear Cauchy Problems with Non-dense Domain
No full textThe main purpose of this chapter is to present a comprehensive semilinear theory that will allow us to study the properties of solutions of the non-densely defined Cauchy problems, such as existence and uniqueness of a maximal semiflow, positivity, Lipschitz perturbation, differentiability with respect to the state variable, time differentiability, classical solutions, stability of equilibria, etc
Le traitement de l’entérite chronique hypertrophiante des Bovidés par les sulfones
No full textVerge Jean, Goret Pierre, Cauchy Laurent. Le traitement de l’entérite chronique hypertrophiante. In: Bulletin de l'Académie Vétérinaire de France tome 104 n°2, 1951. pp. 97-99
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Integrated Semigroups and Cauchy Problems with Non-dense Domain
No full textThe goal of this chapter is to introduce the integrated semigroup theory and use it to investigate the existence and uniqueness of integrated (mild) solutions of the nonhomogeneous Cauchy problems when the domain of the linear operator A is not dense in the state space and A is not a Hille-Yosida operator
Pierre Dugac, Les fondements de l'analyse de Cauchy à Braire
No full textPierre Dugac, Les fondements de l'analyse de Cauchy à Braire. In: Revue d'histoire des sciences, tome 32, n°3, 1979. pp. 286-288
Pierre Dugac, Les fondements de l'analyse de Cauchy à Braire
No full textPierre Dugac, Les fondements de l'analyse de Cauchy à Braire. In: Revue d'histoire des sciences, tome 32, n°3, 1979. pp. 286-288
A class of abstract quasi-linear evolution equations of second order
No full textIn this paper we study the abstract quasi-linear evolution equation of second order
formula here
in a general banach space z. it is well-known that the abstract quasi-linear theory due to kato [10, 11] is widely applicable to quasi-linear partial differential equations of second order and that his theory is based on the theory of semigroups of class (C0). (for example, see the work of hughes et al. [9] and heard [8].) however, even in the special case where a (t,w, v) = a is independent of (t, w, v), it is found in [2] and [14] that there exist linear partial differential equations of second order for which cauchy problems are not solvable by the theory of semigroups of class (C0) but fit into the mould of well-posed problems where the solution and its derivative depend continuously on the initial data if the initial condition is measured in the graph norm of a suitable power of a. (see also work by krein and khazan [13] and fattorini [6, chapter 8].) this kind of cauchy problem has recently been studied extensively, using the theory of integrated semigroups or regularized semigroups. the theory of integrated semigroups was studied intensively by arendt [1] and that of regularized semigroups was initiated by da prato [3] and renewed by davies and pang [4]. for the theory of regularized semigroups we refer the reader to [5] and [16].
(u(t),v(t))' = Ãu(t)(u(t),v(t)) for t∈[0,T] and (u(0),v(0)) = (φ,ψ)
in a suitable Banach space X, where for each solution w of equation (1.1) the matrix operator Aw(t) in X is defined by Aw(t)(u,v)=(v,A(t,w(t),w'(t)) u). We are here interested in studying the case where each matrix operator Aw(t) is the (complete infinitesimal) generator of a regularized semigroup on X. In Section 3 we set up basic hypotheses on the operators appearing in equation (1.1), and prove a fundamental existence and uniqueness theorem (Theorem 3.6) for the Cauchy problem (1.1). The proof is based on the theory of regularized evolution operators developed by the
author [15], and a method of successive approximations proposed by Kobayasi and Sanekata [12] is applied to construct a unique twice continuously differentiable function u satisfying equation (1.1).
Our formulation includes the abstract quasi-linear wave equation of Kirchhoff
type
u"(t)+m(|A1/2u(t)|2)Au(t)=0 (1.2)
in a real Hilbert space H, where A is a nonnegative selfadjoint operator in H. Section 4 presents a regularized semigroup theoretical approach to the local solvability of equation (1.2) in the `degenerate case' where the function m(r) has zeros (Theorems 4.1 and 4.2), by using the result obtained in Section 3. In Section 2 we summarize some results on the generation of a regularized evolution operator associated with the linearized equation of (1.1), under the `regularized stability ' condition, and show that the family of matrix operators used to solve the linearized equation (1.2) satisfies the regularized stability condition. This fact will be useful for our arguments in Section 4.</p
Le traitement de l'entérite chronique hypertrophiante des Bovidés par la streptomycine
No full textCauchy Laurent, Goret Pierre, Mérieux Charles, Verge Jean. Le traitement de l’entérite chronique hyperthrophiante des Bovidés par la streptomycine. In: Bulletin de l'Académie Vétérinaire de France tome 104 n°2, 1951. pp. 93-95
Recherches sur le traitement des mammites des Vaches laitières par la pénicilline
No full textVerge Jean, Saurat Pierre, Groulade Paul, Gaumont R., Renard Pierre, Cauchy Laurent. Recherches sur le traitement des mammites des Vaches laitières par la pénicilline. In: Bulletin de l'Académie Vétérinaire de France tome 101 n°9, 1948. pp. 355-360
Sur la publication du dernier volume des œuvres d'Augustin Cauchy
No full textSUMMARY. — Description of the 27th and last volume of the Cauchy's Complete Works, edited and introduced by René Taton. Analysis of the Memoirs and Reports included here, and also the joined documentation. These texts and documents given to the disposal of the scientists ought to facilitate, it seems, a synthetic study about one of the greatest XlXth Century mathematicians,- Century where are the principal bases of the Analysis in our days.RÉSUMÉ. — Description du 27e et dernier tome des Œuvres complètes de Cauchy, édité et préfacé par René Taton. Analyse des Mémoires et Rapports qui y sont reproduits, ainsi que de l'Annexe documentaire. Les textes et les matériaux mis ainsi à la disposition des chercheurs devraient permettre une étude de synthèse sur l'un des plus grands mathématiciens du XIXe siècle, siècle où l'Analyse, aujourd'hui, trouve ses principaux fondements.Dugac Pierre. Sur la publication du dernier volume des œuvres d'Augustin Cauchy. In: Revue d'histoire des sciences, tome 28, n°1, 1975. pp. 75-83
Cauchy-based modelling in cementitious materials technology
No full textCauchy paved the way for constructing models in concrete technology, and elsewhere. He determined the (non-flat) surface area in 3D by measuring random total projections. Analogously, he determined the length of a curved line in 2D by way of measuring the total projections. The paper will present the mathematical expressions, because in many branches of concrete technology, modelling is found based on such Cauchy concepts. These branches - fractography in compression, tension or shear, fibre reinforcement and permeability estimation - will briefly be mentioned to demonstrate this. It has been found that, for the discussed fields of engineering relevance, major model parameters for cementitious materials are similar to those developed by Cauchy in the 19th century. In the paper some previous investigations concerning fractography, fibre reinforcement and fracture roughness will be summarized but basically a new development on porosimetry will be presented. Particularly a new achievement of successful implementation of the methodology (also based on Cauchy) for optimizing permeability estimation will be discussed.Applied Mechanic
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