On A Class Of Doubly Nonlinear Evolution Equations

Colli, Pierluigi; Visintin, Augusto

doi:10.1080/03605309908820706

Cited by 166 publications

(174 citation statements)

References 10 publications

Supporting

Mentioning

170

Contrasting

Order By: Relevance

“…Note that existence results for this class of equation have been obtained in [3,7,8] for more restrictive vector field a. A work is in progress in this direction.…”

Section: Conclusion and Possible Extensionsmentioning

confidence: 99%

Numerical analysis of nonlinear elliptic-parabolic equations

Maitre

2002

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract. This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern's iteration for nonexpansive operators (Bauschke, 1996;Halpern, 1967;Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995;Kačur, 1999).Mathematics Subject Classification. 65M12, 35K65, 35K55, 65N22.

show abstract

“…Note that existence results for this class of equation have been obtained in [3,7,8] for more restrictive vector field a. A work is in progress in this direction.…”

Section: Conclusion and Possible Extensionsmentioning

confidence: 99%

Numerical analysis of nonlinear elliptic-parabolic equations

Maitre

2002

ESAIM: M2AN

View full text Add to dashboard Cite

show abstract

“…Using an implicit time scheme such as (1.5) to solve doubly nonlinear evolutions in reflexive Banach spaces has been carried out with great success; see [2,4,11,12,16,27,31]. In our view, the main insight that makes this approach work is a certain compactness feature of weak solutions that we now explore.…”

Section: Weak Solutionsmentioning

confidence: 99%

A doubly nonlinear evolution for the optimal Poincaré inequality

Hynd

Lindgren

2016

Calc. Var.

View full text Add to dashboard Cite

We study the large time behavior of solutions of the PDE |v t | p−2 v t = ∆ p v. A special property of this equation is that the Rayleigh quotient Ω |Dv(x, t)| p dx/ Ω |v(x, t)| p dx is nonincreasing in time along solutions. As t tends to infinity, this ratio converges to the optimal constant in Poincaré's inequality. Moreover, appropriately scaled solutions converge to a function for which equality holds in this inequality. An interesting limiting equation also arises when p tends to infinity, which provides a new approach to approximating ground states of the infinity Laplacian.

show abstract

“…We already know that the weak equation (6.2) is equivalent to the PDE the mutually orthogonal spaces 8) and the functionals…”

Section: Single-scale Formulation (Homogenization)mentioning

confidence: 99%

“…The homogenization of several other quasilinear equations may also be studied, including doubly-nonlinear systems of the form 6) with α and γ as above. Existence of a solution for an associated boundary-and initial-value problem was proved in [8].…”

Section: Introductionmentioning

confidence: 99%

Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

Nandakumaran

Visintin

2015

Nonlinear Analysis: Theory, Methods & Applications

View full text Add to dashboard Cite

This work deals with the homogenization of an initial-and boundary-value problem for the doubly-nonlinear systemHere ε is a positive parameter, and the prescribed mappings α and γ are maximal monotone with respect to the first variable and periodic with respect to the second one. The inclusions (0.2) and (0.3) are here formulated as null-minimization principles, via the theory of Fitzpatrick [MR 1009594]. As ε → 0, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved. (2000): 35B27, 35K60, 49J40, 78M40. AMS Classification

show abstract

On A Class Of Doubly Nonlinear Evolution Equations

Cited by 166 publications

References 10 publications

Numerical analysis of nonlinear elliptic-parabolic equations

Numerical analysis of nonlinear elliptic-parabolic equations

A doubly nonlinear evolution for the optimal Poincaré inequality

Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

Contact Info

Product

Resources

About