The Experts below are selected from a list of 4749 Experts worldwide ranked by ideXlab platform
Rodica Toader - One of the best experts on this subject based on the ideXlab platform.
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a model for the quasi static growth of brittle fractures existence and approximation results
Archive for Rational Mechanics and Analysis, 2002Co-Authors: Gianni Dal Maso, Rodica ToaderAbstract:We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G. A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an Absolutely Continuous Function of time, although we cannot exclude the possibility that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time-discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the Continuous time evolution.
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a model for the quasi static growth of a brittle fracture existence and approximation results
arXiv: Analysis of PDEs, 2001Co-Authors: Gianni Dal Maso, Rodica ToaderAbstract:We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of a brittle fracture proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an Absolutely Continuous Function of time, although we can not exclude that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the Continuous time evolution.
Gianni Dal Maso - One of the best experts on this subject based on the ideXlab platform.
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a model for the quasi static growth of brittle fractures existence and approximation results
Archive for Rational Mechanics and Analysis, 2002Co-Authors: Gianni Dal Maso, Rodica ToaderAbstract:We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G. A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an Absolutely Continuous Function of time, although we cannot exclude the possibility that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time-discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the Continuous time evolution.
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a model for the quasi static growth of a brittle fracture existence and approximation results
arXiv: Analysis of PDEs, 2001Co-Authors: Gianni Dal Maso, Rodica ToaderAbstract:We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of a brittle fracture proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an Absolutely Continuous Function of time, although we can not exclude that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the Continuous time evolution.
Maliheh Hosseini - One of the best experts on this subject based on the ideXlab platform.
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projections in the convex hull of three isometries on Absolutely Continuous Function spaces
Bulletin of the Malaysian Mathematical Sciences Society, 2021Co-Authors: Maliheh Hosseini, A JimenezvargasAbstract:In this paper, we prove that any projection in the convex hull of three surjective linear isometries on $$\mathrm {AC}(X)$$ is a generalized bi-circular projection, where $$\mathrm {AC}(X)$$ denotes the Banach space of all Absolutely Continuous Functions on a compact subset of $$\mathbb {R}$$ with at least two points. We also show that the trivial projections are the only projections on $$\mathrm {AC}(X)$$ which can be represented as the average of three surjective linear isometries.
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Projections in the convex hull of two isometries of Absolutely Continuous Function spaces
Positivity, 2020Co-Authors: Maliheh HosseiniAbstract:In this paper we provide a complete description of projections in the convex hull of two surjective linear isometries (carrying a weighted composition operator form) on Absolutely Continuous Function space AC ( X , E ), where X is a compact subset of $$\mathbb R$$ R with at least two points and E is a strictly convex normed space. Among the consequences of the main result, it is shown that generalized bi-circular projections are the only projections on AC ( X ) expressed as the convex combination of two surjective linear isometries, and an affirmative answer is given to the question in Botelho and Jamison (Canad Math Bull 53:398–403, 2010) for such spaces.
Elijah Liflyand - One of the best experts on this subject based on the ideXlab platform.
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asymptotic behavior of the fourier transform of a Function of bounded variation
2017Co-Authors: Elijah LiflyandAbstract:A recent result on the asymptotic behavior of the sine Fourier transform of an arbitrary locally Absolutely Continuous Function of bounded variation is extended to the case of several variables. For this, the initial one-dimensional result is reconsidered and refined. To even one-dimensional asymptotics and their multidimensional generalizations, a new balance operator is introduced.
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Integrability spaces for the Fourier transform of a Function of bounded variation
Journal of Mathematical Analysis and Applications, 2016Co-Authors: Elijah LiflyandAbstract:Abstract New relations between the Fourier transform of a Function of bounded variation and the Hilbert transform of its derivative are revealed. After various preceding works of the last 25 years where the behavior of the Fourier transform has been considered on specific subspaces of the space of Functions of bounded variation, in this paper such problems are considered on the whole space of Functions of bounded variation. The widest subspaces of the space of Functions of bounded variation are studied for which the cosine and sine Fourier transforms are integrable. The main result of the paper is an asymptotic formula for the sine Fourier transform of an arbitrary locally Absolutely Continuous Function of bounded variation. Interrelations of various Function spaces are studied, in particular, the sharpness of Hardy's inequality is established and the inequality itself is strengthened in certain cases. A way to extend the obtained results to the radial case is shown.
Ghaus Ur Rahman - One of the best experts on this subject based on the ideXlab platform.
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fractional calculus and fractional differential equations in nonreflexive banach spaces
Communications in Nonlinear Science and Numerical Simulation, 2015Co-Authors: Ravi P Agarwal, Vasile Lupulescu, Donal Oregan, Ghaus Ur RahmanAbstract:Abstract In this paper we establish an existence result for the fractional differential equation D p α y ( t ) = f ( t , y ( t ) ) , y ( 0 ) = y 0 , where D p α y ( · ) is a fractional pseudo-derivative of a weakly Absolutely Continuous and pseudo-differentiable Function y(·) : T → E, the Function f (t, ·) : T × E → E is weakly–weakly sequentially Continuous for every t ∈ T and f (·, y(·)) is Pettis integrable for every weakly Absolutely Continuous Function y(·) : T → E, T is a bounded interval of real numbers and E is a nonreflexive Banach space.
