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Measurable solutions for elliptic and evolution inclusions
249 Havenside Court, Grantsville, Utah 84029, USA |
This paper obtains existence of random variable solutions to elliptic and evolution inclusions. As a special case, surprising theorems are obtained for the quasistatic problems. A new existence theorem is also presented for evolution inclusions with set valued operators dependent on elements of a measurable space.
References:
| [1] |
K. T. Andrews, K. L. Kuttler, J. Li and M. Shillor,
Measurable solutions for elliptic inclusions and quasistatic problems, Comput. Math. Appl., 77 (2019), 2869-2882.
doi: 10.1016/j.camwa.2018.09.025. |
| [2] |
A. Bensoussan and R. Temam,
Équations stochastiques du type Navier-Stokes, J. Functional Analysis, 13 (1973), 195-222.
doi: 10.1016/0022-1236(73)90045-1. |
| [3] |
H. Brezis,
Équations et inéquations non lin éaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble), 18 (1968), 115-175.
doi: 10.5802/aif.280. |
| [4] |
Z. Denkowski, S. Migórski and N. S. Papageorgiu, An Introduction to Nonlinear Analysis: Theory, Kluwer Academic Publishers, Boston, MA, 2003; Somerville, MA, (2002).
doi: 10.1007/978-1-4419-9158-4. |
| [5] |
W. Han and M. Sofonea, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity,
Vol. 30, Studies in Advanced Mathematics, American Mathematical Society, Providence, RI;
International Press, Somerville, MA, 2002. |
| [6] |
S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis. Vol. I. Theory. Mathematics and its Applications, Vol. 419, Kluwer Academic Publishers, Dordrecht, 1997. |
| [7] |
K. L. Kuttler, J. Li and M. Shillor, A general product measurability theorem with applications to variational inequalities, Electron. J. Differential Equations, 90 (2016), 12 pp. |
| [8] |
K. L. Kuttler and M. Shillor, Product measurability with applications to a stochastic contact problem with friction, Electron. J. Differential Equations, 258 (2014), 29 pp. |
| [9] |
K. Kuttler, Non-degenerate implicit evolution inclusions, Electron. J. Differential Equations, 34 (2000), 20 pp. |
| [10] |
K. L. Kuttler and M. Shillor,
Set-valued pseudomonotone maps and degenerate evolution inclusions, Commun. Contemp. Math., 1 (1999), 87-123.
doi: 10.1142/S0219199799000067. |
| [11] |
J.-L. Lions, Quelques Méthods de Résolution des Problèmes aux Limites Non Linéaires, Dunod; Gauthier-Villars, Paris, 1969. |
| [12] |
S. Migórski, A. Ochal and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems, Vol. 26, Advances in Mechanics and Mathematics, Springer, New York, 2013.
doi: 10.1007/978-1-4614-4232-5. |
| [13] |
M. Shillor, M. Sofonea and J. J. Telega, Models and Analysis of Quasistatic Contact, Vol. 655, Lecture Notes in Physics, Springer, Berlin, Heidelberg, 2004.
doi: 10.1007/b99799. |
| [14] |
M.Sofonea, W. Han and M. Shillor, Analysis and Approximation of Contact Problems with Adhesion or Damage, Vol. 276, Pure and Applied Mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2006. |
show all references
References:
| [1] |
K. T. Andrews, K. L. Kuttler, J. Li and M. Shillor,
Measurable solutions for elliptic inclusions and quasistatic problems, Comput. Math. Appl., 77 (2019), 2869-2882.
doi: 10.1016/j.camwa.2018.09.025. |
| [2] |
A. Bensoussan and R. Temam,
Équations stochastiques du type Navier-Stokes, J. Functional Analysis, 13 (1973), 195-222.
doi: 10.1016/0022-1236(73)90045-1. |
| [3] |
H. Brezis,
Équations et inéquations non lin éaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble), 18 (1968), 115-175.
doi: 10.5802/aif.280. |
| [4] |
Z. Denkowski, S. Migórski and N. S. Papageorgiu, An Introduction to Nonlinear Analysis: Theory, Kluwer Academic Publishers, Boston, MA, 2003; Somerville, MA, (2002).
doi: 10.1007/978-1-4419-9158-4. |
| [5] |
W. Han and M. Sofonea, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity,
Vol. 30, Studies in Advanced Mathematics, American Mathematical Society, Providence, RI;
International Press, Somerville, MA, 2002. |
| [6] |
S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis. Vol. I. Theory. Mathematics and its Applications, Vol. 419, Kluwer Academic Publishers, Dordrecht, 1997. |
| [7] |
K. L. Kuttler, J. Li and M. Shillor, A general product measurability theorem with applications to variational inequalities, Electron. J. Differential Equations, 90 (2016), 12 pp. |
| [8] |
K. L. Kuttler and M. Shillor, Product measurability with applications to a stochastic contact problem with friction, Electron. J. Differential Equations, 258 (2014), 29 pp. |
| [9] |
K. Kuttler, Non-degenerate implicit evolution inclusions, Electron. J. Differential Equations, 34 (2000), 20 pp. |
| [10] |
K. L. Kuttler and M. Shillor,
Set-valued pseudomonotone maps and degenerate evolution inclusions, Commun. Contemp. Math., 1 (1999), 87-123.
doi: 10.1142/S0219199799000067. |
| [11] |
J.-L. Lions, Quelques Méthods de Résolution des Problèmes aux Limites Non Linéaires, Dunod; Gauthier-Villars, Paris, 1969. |
| [12] |
S. Migórski, A. Ochal and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems, Vol. 26, Advances in Mechanics and Mathematics, Springer, New York, 2013.
doi: 10.1007/978-1-4614-4232-5. |
| [13] |
M. Shillor, M. Sofonea and J. J. Telega, Models and Analysis of Quasistatic Contact, Vol. 655, Lecture Notes in Physics, Springer, Berlin, Heidelberg, 2004.
doi: 10.1007/b99799. |
| [14] |
M.Sofonea, W. Han and M. Shillor, Analysis and Approximation of Contact Problems with Adhesion or Damage, Vol. 276, Pure and Applied Mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2006. |
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