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Limit of the infinite horizon discounted Hamilton-Jacobi equation
Lipschitz continuous data dependence of sweeping processes in BV spaces
1. | Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ-11567 Praha 1 |
2. | Department of Mathematics / M6, Technische Universität München, Boltzmannstr. 3, 85748 Garching b. München, Germany |
References:
[1] |
G. Aumann, "Reelle Funktionen," Springer-Verlag, New York, 1954. |
[2] |
M. Brokate, P. Krejčí and H. Schnabel, On uniqueness in evolution quasivariational inequalities, J. Convex Anal., 11 (2004), 111-130. |
[3] |
A. L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part I - yield criteria and flow rules for porous ductile media, J. Engrg. Mater. Tech., 99 (1977), 2-15.
doi: 10.1115/1.3443401. |
[4] |
P. Krejčí and P. Laurençot, Generalized variational inequalities, J. Convex Anal., 9 (2002), 159-183. |
[5] |
P. Krejčí and M. Liero, Rate independent Kurzweil processes, Appl. Math., 54 (2009), 117-145.
doi: 10.1007/s10492-009-0009-5. |
[6] |
J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J., 7(82) (1957), 418-449. |
[7] |
A. Mielke and F. Theil, On rate-independent hysteresis models, NoDEA Nonlinear Differential Equations Appl., 11 (2004), 151-189. |
[8] |
J.-J. Moreau, Problème d'évolution associé à un convexe mobile d'un espace hilbertien, C. R. Acad. Sci. Paris Sér. A-B, 276 (1973), A791-A794. |
[9] |
J.-J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space, J. Differential Eq., 26 (1977), 347-374.
doi: 10.1016/0022-0396(77)90085-7. |
[10] |
V. Recupero, On locally isotone rate independent operators, Applied Mathematics Letters, 20 (2007), 1156-1160.
doi: 10.1016/j.aml.2006.10.006. |
[11] |
V. Recupero, $BV$-extension of rate independent operators, Math. Nachr., 282 (2009), 86-98.
doi: 10.1002/mana.200610723. |
[12] |
V. Recupero, $BV$-solutions of rate independent variational inequalities,, To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci., ().
|
[13] |
U. Stefanelli, A variational characterization of rate-independent evolution, Math. Nachr., 282 (2009), 1492-1512.
doi: 10.1002/mana.200810803. |
[14] |
M. Tvrdý, Regulated functions and the Perron-Stieltjes integral, Čas. pěst. Mat., 114 (1989), 187-209. |
show all references
References:
[1] |
G. Aumann, "Reelle Funktionen," Springer-Verlag, New York, 1954. |
[2] |
M. Brokate, P. Krejčí and H. Schnabel, On uniqueness in evolution quasivariational inequalities, J. Convex Anal., 11 (2004), 111-130. |
[3] |
A. L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part I - yield criteria and flow rules for porous ductile media, J. Engrg. Mater. Tech., 99 (1977), 2-15.
doi: 10.1115/1.3443401. |
[4] |
P. Krejčí and P. Laurençot, Generalized variational inequalities, J. Convex Anal., 9 (2002), 159-183. |
[5] |
P. Krejčí and M. Liero, Rate independent Kurzweil processes, Appl. Math., 54 (2009), 117-145.
doi: 10.1007/s10492-009-0009-5. |
[6] |
J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J., 7(82) (1957), 418-449. |
[7] |
A. Mielke and F. Theil, On rate-independent hysteresis models, NoDEA Nonlinear Differential Equations Appl., 11 (2004), 151-189. |
[8] |
J.-J. Moreau, Problème d'évolution associé à un convexe mobile d'un espace hilbertien, C. R. Acad. Sci. Paris Sér. A-B, 276 (1973), A791-A794. |
[9] |
J.-J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space, J. Differential Eq., 26 (1977), 347-374.
doi: 10.1016/0022-0396(77)90085-7. |
[10] |
V. Recupero, On locally isotone rate independent operators, Applied Mathematics Letters, 20 (2007), 1156-1160.
doi: 10.1016/j.aml.2006.10.006. |
[11] |
V. Recupero, $BV$-extension of rate independent operators, Math. Nachr., 282 (2009), 86-98.
doi: 10.1002/mana.200610723. |
[12] |
V. Recupero, $BV$-solutions of rate independent variational inequalities,, To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci., ().
|
[13] |
U. Stefanelli, A variational characterization of rate-independent evolution, Math. Nachr., 282 (2009), 1492-1512.
doi: 10.1002/mana.200810803. |
[14] |
M. Tvrdý, Regulated functions and the Perron-Stieltjes integral, Čas. pěst. Mat., 114 (1989), 187-209. |
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