1,721,235 research outputs found
Inverse and direct problems for nonautonomous degenerate integrodifferential equations of parabolic type with Dirichlet boundary conditions
No full textThis paper deals with inverse and direct problems related to linear degenerate integrodifferential equations of parabolic type. The study of the direct problem is highly affected by the related inverse problems so that the results of the direct problems are just those needed to solve – locally in time – the inverse one. The latter is concerned with recovering – in a Hölder class – a memory kernel depending on time only
Singular integro-differential equations of parabolic type
No full textWe study a linear singular first-order integro-differential Cauchy problems in Banach spaces. Singular here means that the integro differential equation is not in normal form neither can it be reduced to such a form. We generalize to this context some existence and uniqueness theorems known for differential equations. Particular attention is given to single out the optimal regularity properties of solutions as well as to point out several explicit applications related tosingular partial integrodifferential of parabolic type
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.
Singular evolution integro-differential equations with kernels defined on bounded intervals
No full textWe study linear singular first-order integro-differential Cauchy problems in Banach spaces. The adjective “singular” means here that the integro-differential equation is not in normal form neither can it be reduced to such a form. We generalize some existence and uniqueness theorems proved in [5] for kernels defined on the entire half-line R+ to the case of kernels defined on bounded intervals removing the strict assumption that the kernel should be Laplace-transformable.
Particular attention is paid to single out the optimal regularity properties of solutions as well as to point out several explicit applications relative to singular partial integro-differential equations of parabolic and hyperbolic type
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
On the solvability and the maximal regularity of complete abstract differential equations of elliptic type
No full textIn this paper we give some new results on complete abstract second order differential equations of elliptic type in a Banach space. Existence, uniqueness and maximal regularity of the strict solution are proved under some natural assumptions generalizing previous theorems on the subjec
On the solvability of complete abstract differential equations of elliptic type
No full textIn this work we give some new results on complete abstract second order differential equations of elliptic type in a Banach space. The existence and the uniqueness of the strict solution are proved under some natural assumptions generalising previous theorems on the subjec
Degenerate integrodifferential equation of parabolic type with Robin boundary conditions: L^2-theory
No full textThis paper is devoted to solving a degenerate parabolic integrodifferential equation with the Robin boundary condition. We begin with solving the equation without the integral delay term. For that purpose we introduce some new unknown function following Favini and Yagi [4] and construct the fundamental solution to the equation to be satisfied by it by the method of Kato and Tanabe [5]. Using this fundamental solution we transform the original problem to an easily solvable integral equation for the time derivative of the new unknown function
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