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Weighted Energy-Dissipation approach to semilinear gradient flows with state-dependent dissipation
Published 4 Apr 2024 in math.AP | (2404.03370v1)
Abstract: We investigate the Weighted Energy-Dissipation variational approach to semilinear gradient flows with state-dependent dissipation. A family of parameter-dependent functionals defined over entire trajectories is introduced and proved to admit global minimizers. These global minimizers correspond to solutions of elliptic-in-time regularizations of the limiting causal problem. By passing to the limit in the parameter we prove that such global minimizers converge, up to subsequences, to a solution of the gradient flow.
- H. Brezis. Opérateur maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. (French) North-Holland Mathematics Studies, no. 5. Notas de Matemática (50). North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973.
- G. Dal Maso. An introduction to Γnormal-Γ\Gammaroman_Γ-convergence. Progress in Nonlinear Differential Equations and their Applications, 8. Birkhäuser Boston Inc., Boston, MA, 1993.
- E. De Giorgi. Conjectures concerning some evolution problems. Duke Math. J. 81 (1996), 255–268.
- L. C. Evans. Partial differential equations. Graduate Studies in Mathematics, volume 19. American Mathematical Society, Providence, 1998.
- T. Ilmanen. Elliptic regularization and partial regularity for motion by mean curvature. Memoirs of the American Mathematical Society, number 520. American Mathematical Society, Providence, 1994.
- N. Hirano. Existence of periodic solutions for nonlinear evolution equations in Hilbert spaces. Proc. Amer. Math. Soc. 120 (1994), 185–192.
- U. Stefanelli. The De Giorgi conjecture on elliptic regularization. Math. Models Methods Appl. Sci. 21 (2011), 1377–1394.
- E. Zeidler. Nonlinear functional analysis and its applications II/B. Springer-Verlag, New York, 1990.
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