1,721,075 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.
Singular integro-differential equations of parabolic type and inverse problems
No full textWe prove a global existence and uniqueness result for the recovery of unknown scalar kernels in linear singular first-order integro-differential initial-boundary value problems in Banach spaces. To this end use is made of suitable weighted Lp-spaces. Finally, we give a few applications to explicit singular partial integro-differential equations of parabolic type
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
Exponential attractors for semiconductor equations
No full textThis paper studies the asymptotic behaviour of solutions to the classical semiconductor equations due to Shockley. We will construct not only global solutions but also exponential attractors for the dynamical system determined from the Cauchy problem. Exponential attractors — such a notion was introduced by Eden, Foias, Nicolaenko and Temam — are positively invariant sets which contain the global attractor, have finite fractal dimensions and attract every trajectory in an exponential rate
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
Boundary flux identification for thermal systems with memory
No full textIl convegno concerne ricerche su problemi inversi, di identificazione ed equazioni con memoria
Fourth order ordinary differential operators with general Wentzell boundary conditions
No full textWe consider the fourth order ordinary differential operator Au:= (au″)″ with boundary conditions (eqution found) and one of uʹ(j); u″(j) vanishes for j = 0, 1: Here β0 \u3c 0 \u3c β1: Then A is essentially selfadjoint and bounded below on the Hilbert space H = L2(0, 1) ⊕ C2w, the completion of C[0, 1] under the inner product (eqution found) where wj:= (–1)j+1/Bj for j = 0, 1. Applications to partial differential equations are given
Esistenza e unicità globale per un problema inverso integrodifferenziale parabolico semilineare
No full textWe consider the problem of recovering a convolution kernel, together with the solution, in a semilinear integrodifferential mixed initial-boundary value problem of parabolic type. We present some results of local existence, global uniqueness and, under proper further assumptions, global existence
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
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
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