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Well Posedness for Pressureless Flow
Communications in Mathematical Physics, 2001This paper considers the one-dimensional pressureless gases and studies the uniqueness of weak solutions when the initial data is a Radon measure. It is shown that besides the Oleinik entropy condition, it is important to require the energy to be weakly continuous initially; and without this energy condition, the weak solution satisfying the Oleinik ...
Huang, Feimin, Wang, Zhen
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Well Posedness and Inf-Convolution
Journal of Optimization Theory and Applications, 2018We prove that the notion of Tykhonov well-posed problems is stable under the operation of inf-convolution. We deal with lower semicontinuous functions (not necessarily convex) defined on a metric magma. Several applications are given, in particular to the study of the map argmin.
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Well-posedness and weak well-posedness in Banach spaces
1997Let (X, ‖ · ‖) be a Banach space. Let Φ be the class of all continuous linear (affine) functionals. A function f is Φ-convex if and only if it is convex and lower semi-continuous.
Diethard Pallaschke, Stefan Rolewicz
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Well-Posedness of Dynamic Cosserat Plasticity
Applied Mathematics and Optimization, 2007We investigate the regularizing properties of generalized continua of micropolar type for dynamic elasto-plasticity. To this end we propose an extension of classical infinitesimal elasto-plasticity to include consistently non-dissipative micropolar effects and we show that the dynamic model allows for a unique, global in-time solution of the ...
Neff, Patrizio, Chełmiński, Krzysztof
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Well Posedness for Multilane Traffic Models
ANNALI DELL'UNIVERSITA' DI FERRARA, 2006In the present study the authors consider continuum models for multilane traffic flow. Typically, continuum models for multilane traffic are based on a system of conservation laws with source terms. In each equation, the convective part describes the intra-lane dynamics, while the right-hand side models the interplay between adjacent lanes.
COLOMBO, Rinaldo Mario, CORLI ANDREA
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Well Posedness and Optimization Problems
2007This contribution is in the field of Game Theory and Nash equilibria. The property of Tihkonov well posedness is analyzed in relation to other well posedeness properties which are ordinal, a very important property for games because it emphasizes the fact that players’ decisions are expressed by preferences and not by a special choice of utility ...
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Potential games and well-posedness properties
Optimization, 2008The aim of this article is to study potential games which are a special class of games, in fact their properties are dictated by a single function called the potential function. We consider Tikhonov well-posedness and other well-posedness properties introduced by the authors in Margiocco et al. (Margiocco, M., Patrone, F.
MARGIOCCO M, PUSILLO, ANGELA LUCIA
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1999
Mathematical modeling of soil venting leads to a system of partial differential equations. Before starting all computations, one must do the qualitative and quantitative analysis of solutions for corresponding problems (at least in simple situations as the study cases).
Horst H. Gerke +4 more
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Mathematical modeling of soil venting leads to a system of partial differential equations. Before starting all computations, one must do the qualitative and quantitative analysis of solutions for corresponding problems (at least in simple situations as the study cases).
Horst H. Gerke +4 more
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On Well-Posedness of Relay Systems
IFAC Proceedings Volumes, 2001Abstract In this paper we study the well-posedness (existence and uniqueness of solutions) of linear relay systems with respect to two different solution concepts. We derive necessary and sufficient conditions for well-posedness in the sense of Filippov of linear systems of relative degree one and two in closed loop with relay feedback.
Pogromsky, A.Y. +2 more
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2010
We recall the concept of porosity [10, 26, 27, 84, 97, 98, 112]. Let (Y, d) be a complete metric space. We denote by Bd(y, r) the closed ball of center \(y\ \in\ Y,\) and radius r > 0. A subset \(E \subset Y\) is called porous with respect to d (or just porous if the metric is understood) if there exist \(\alpha \in\) (0, 1] and r0 > 0 such that for ...
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We recall the concept of porosity [10, 26, 27, 84, 97, 98, 112]. Let (Y, d) be a complete metric space. We denote by Bd(y, r) the closed ball of center \(y\ \in\ Y,\) and radius r > 0. A subset \(E \subset Y\) is called porous with respect to d (or just porous if the metric is understood) if there exist \(\alpha \in\) (0, 1] and r0 > 0 such that for ...
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