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Scott J Spector - One of the best experts on this subject based on the ideXlab platform.

  • an Existence Theory for nonlinear elasticity that allows for cavitation
    Archive for Rational Mechanics and Analysis, 1995
    Co-Authors: Stefan Muller, Scott J Spector
    Abstract:

    In this paper the Existence of minimizers in nonlinear elasticity is established under assumptions on the stored energy that permit the formation of new holes in the body. Such cavities have been observed in experiments on elastomers, and a mathematical Theory for radially symmetric cavities has been developed by Ball. Here the full three-dimensional problem is considered and an additional, physically motivated, energy term that is proportional to the area of the boundary of the deformed body is included. The minimizers lie in a subclass of those maps in W1, p, 2one-to-one almost everywhere and preserve orientation. Roughly speaking, this subclass consists of those maps in which cavities in one part of the body are not filled by material from other parts of the body. Such maps are shown to be much more regular than expected. In particular, some ideas of Sverak are used to show that each map in this subclass has a representative which is continuous outside a set of Hausdorff dimension 3 — p and that this representative also satisfies Lusin's condition (N), i.e., it maps Lebesgue null sets onto such sets. It is also shown that the distributional Jacobian of such a map is a measure which is the sum of a measure that is absolutely continuous with respect to Lebesgue measure and (at most) a countable number of Dirac measures.

Ravi P. Agarwal - One of the best experts on this subject based on the ideXlab platform.

Fahd Jarad - One of the best experts on this subject based on the ideXlab platform.

  • Existence Theory and numerical solutions to smoking model under caputo fabrizio fractional derivative
    Chaos, 2019
    Co-Authors: Sajjad Ali Khan, Kamal Shah, Gul Zaman, Fahd Jarad
    Abstract:

    In this paper, taking fractional derivative due to Caputo and Fabrizo, we have investigated a biological model of smoking type. By using Sumudu transform and Picard successive iterative technique, we develop the iterative solutions for the considered model. Furthermore, some results related to uniqueness of the equilibrium solution and its stability are discussed utilizing the techniques of nonlinear functional analysis. The dynamics of iterative solutions for various compartments of the model are plotted with the help of Matlab.

  • Existence Theory and numerical solutions to smoking model under caputo fabrizio fractional derivative
    Chaos, 2019
    Co-Authors: Sajjad Ali Khan, Kamal Shah, Gul Zaman, Fahd Jarad
    Abstract:

    In this paper, taking fractional derivative due to Caputo and Fabrizo, we have investigated a biological model of smoking type. By using Sumudu transform and Picard successive iterative technique, we develop the iterative solutions for the considered model. Furthermore, some results related to uniqueness of the equilibrium solution and its stability are discussed utilizing the techniques of nonlinear functional analysis. The dynamics of iterative solutions for various compartments of the model are plotted with the help of Matlab.In this paper, taking fractional derivative due to Caputo and Fabrizo, we have investigated a biological model of smoking type. By using Sumudu transform and Picard successive iterative technique, we develop the iterative solutions for the considered model. Furthermore, some results related to uniqueness of the equilibrium solution and its stability are discussed utilizing the techniques of nonlinear functional analysis. The dynamics of iterative solutions for various compartments of the model are plotted with the help of Matlab.

Bashir Ahmad - One of the best experts on this subject based on the ideXlab platform.

Stefan Muller - One of the best experts on this subject based on the ideXlab platform.

  • an Existence Theory for nonlinear elasticity that allows for cavitation
    Archive for Rational Mechanics and Analysis, 1995
    Co-Authors: Stefan Muller, Scott J Spector
    Abstract:

    In this paper the Existence of minimizers in nonlinear elasticity is established under assumptions on the stored energy that permit the formation of new holes in the body. Such cavities have been observed in experiments on elastomers, and a mathematical Theory for radially symmetric cavities has been developed by Ball. Here the full three-dimensional problem is considered and an additional, physically motivated, energy term that is proportional to the area of the boundary of the deformed body is included. The minimizers lie in a subclass of those maps in W1, p, 2one-to-one almost everywhere and preserve orientation. Roughly speaking, this subclass consists of those maps in which cavities in one part of the body are not filled by material from other parts of the body. Such maps are shown to be much more regular than expected. In particular, some ideas of Sverak are used to show that each map in this subclass has a representative which is continuous outside a set of Hausdorff dimension 3 — p and that this representative also satisfies Lusin's condition (N), i.e., it maps Lebesgue null sets onto such sets. It is also shown that the distributional Jacobian of such a map is a measure which is the sum of a measure that is absolutely continuous with respect to Lebesgue measure and (at most) a countable number of Dirac measures.