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1
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Second order evolution equations with parameter

100%
Bochenek J., Winiarska T.
Annales Polonici Mathematici
|
1994
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tom 59
|
nr 1
41-52
EN
We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter $h ∈ Ω ⊂ ℝ^m$. Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.
2
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Evolution equations with parameter in the hyperbolic case

88%
Bochenek J., Winiarska T.
Annales Polonici Mathematici
|
1996
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tom 64
|
nr 1
47-60
EN
The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter $h ∈ Ω ⊂ ℝ^m$ in the "hyperbolic" case.
3
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Existence of the fundamental solution of a second order evolution equation

75%
Bochenek J.
Annales Polonici Mathematici
|
1997
|
tom 66
|
nr 1
15-35
EN
We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence ${A_n(t)}$ of bounded operators.
4

Periodic solutions of evolution problem associated with moving convex sets

75%
Castaing C., Monteiro Marques M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
|
tom 15
|
nr 2
99-127
EN
This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form $-Du ∈ N_{C(t)}(u(t)) + f(t,u(t))$ where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, $N_{C(t)}(u(t))$ is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions for this differential inclusion are stated under various assumptions on the moving convex set C(t) and the perturbation f.
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