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1
Content available remote

On an integral transform by R. S. Phillips

100%
Bjon S.
Open Mathematics
|
2010
|
tom 8
|
nr 1
98-113
EN
The properties of a transformation $$ f \mapsto \tilde f_h $$ by R.S. Phillips, which transforms an exponentially bounded C 0-semigroup of operators T(t) to a Yosida approximation depending on h, are studied. The set of exponentially bounded, continuous functions f: [0, ∞[→ E with values in a sequentially complete L c-embedded space E is closed under the transformation. It is shown that $$ (\tilde f_h )\widetilde{_k } = \tilde f_{h + k} $$ for certain complex h and k, and that $$ f(t) = \lim _{h \to 0^ + } \tilde f_h (t) $$, where the limit is uniform in t on compact subsets of the positive real line. If f is Hölder-continuous at 0, then the limit is uniform on compact subsets of the non-negative real line. Inversion formulas for this transformation as well as for the Laplace transformation are derived. Transforms of certain semigroups of non-linear operators on a subset X of an L c-embedded space are studied through the C 0-semigroups, which they define by duality on a space of functions on X.
2
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Numerical schemes for multivalued backward stochastic differential systems

88%
Maticiuc L., Rotenstein E.
Open Mathematics
|
2012
|
tom 10
|
nr 2
693-702
EN
We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: $$dY_t + F(t,X_t ,Y_t ,Z_t )dt \in \partial \phi (Y_t )dt + Z_t dW_t ,$$ where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational inequality in conjunction with Yosida approximation techniques.
3
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Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions

63%
Bader R., Papageorgiou N. S.
Annales Polonici Mathematici
|
2000
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tom 73
|
nr 1
69-92
EN
We consider a quasilinear vector differential equation which involves the p-Laplacian and a maximal monotone map. The boundary conditions are nonlinear and are determined by a generally multivalued, maximal monotone map. We prove two existence theorems. The first assumes that the maximal monotone map involved is everywhere defined and in the second we drop this requirement at the expense of strengthening the growth hypothesis on the vector field. The proofs are based on the theory of operators of monotone type and on the Leray-Schauder fixed point theorem. At the end we present some special cases (including the classical Dirichlet, Neumann and periodic problems), which illustrate the general and unifying features of our work.
4

Periodic solutions for quasilinear vector differential equations with maximal monotone terms

63%
Kourogenis N., Papageorgiou N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1997
|
tom 17
|
nr 1-2
67-81
EN
We consider a quasilinear vector differential equation with maximal monotone term and periodic boundary conditions. Approximating the maximal monotone operator with its Yosida approximation, we introduce an auxiliary problem which we solve using techniques from the theory of nonlinear monotone operators and the Leray-Schauder principle. To obtain a solution of the original problem we pass to the limit as the parameter λ > 0 of the Yosida approximation tends to zero.
5
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On quasistatic inelastic models of gradient type with convex composite constitutive equations

63%
Chełmiński K.
Open Mathematics
|
2003
|
tom 1
|
nr 4
670-689
EN
This article defines and presents the mathematical analysis of a new class of models from the theory of inelastic deformations of metals. This new class, containing so called convex composite models, enlarges the class containing monotone models of gradient type defined in [1]. This paper starts to establish the existence theory for models from this new class; we restrict our investigations to the coercive and linear self-controlling case.
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