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Displaying 1 – 14 of 14

Non-convex perturbations of evolution equations with $m$ -dissipative operators in Banach spaces

Evgenios P. Avgerinos, Nikolaos S. Papageorgiou (1989)

Commentationes Mathematicae Universitatis Carolinae

Nonlinear diffusion equations with perturbation terms on unbounded domains

Kurima, Shunsuke (2017)

Proceedings of Equadiff 14

This paper considers the initial-boundary value problem for the nonlinear diffusion equation with the perturbation term $u_{t} + (- Δ + 1) β (u) + G (u) = g in Ω \times (0, T)$ in an unbounded domain $Ω \subset ℝ^{N}$ with smooth bounded boundary, where $N \in ℕ$ , $T > 0$ , $β$ , is a single-valued maximal monotone function on $ℝ$ , e.g., $β (r) = {| r |}^{q - 1} r (q > 0, q \neq 1)$ and $G$ is a function on $ℝ$ which can be regarded as a Lipschitz continuous operator from ${(H^{1} (Ω))}^{*}$ to ${(H^{1} (Ω))}^{*}$ . The present work establishes existence and estimates for the above problem.

Nonlinear equations in Hilbert space.

Lavrent'ev, I.M., Šćepanović, R. (1986)

Publications de l'Institut Mathématique. Nouvelle Série

Nonlinear Evolution Equations of Soboley-Galpern Type.

Bui An Ton (1976)

Mathematische Zeitschrift

Nonlinear Mappings of Analytic Type in Banach Spaces.

F.E. BROWDER (1970)

Mathematische Annalen

Nonlinear monotone semigroups and viscosity solutions

Samuel Biton (2001)

Annales de l'I.H.P. Analyse non linéaire

Nonlinear nonautonomous partial functional differential BVP.

Chin-Yuan Lin (1994)

Mathematische Annalen

Nonlinear Random Equations with Monotone Operators in Banach Spaces.

Shigeru Itoh (1978)

Mathematische Annalen

Nonlinear random operator equations and inequalities in Banach spaces.

Karamolegos, Antonios, Kravvaritis, Dimitrios (1992)

International Journal of Mathematics and Mathematical Sciences

Nonlinear Variational Inequalities and Maximal Monotone Mappings in Banach Spaces.

F.E. BROWDER (1969)

Mathematische Annalen

Norm-to-weak upper semicontinuous monotone operators are generically strongly continuous.

Veselý, L. (1992)

Acta Mathematica Universitatis Comenianae. New Series

Note on the paper: interior proximal method for variational inequalities on non-polyhedral sets

Alexander Kaplan, Rainer Tichatschke (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we clarify that the interior proximal method developed in [6] (vol. 27 of this journal) for solving variational inequalities with monotone operators converges under essentially weaker conditions concerning the functions describing the "feasible" set as well as the operator of the variational inequality.

Numerical precision for differential inclusions with uniqueness

Jérôme Bastien, Michelle Schatzman (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is $1 / 2$ in general and $1$ when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl’s rheological model, our estimates in maximum norm do not depend on spatial dimension.

Numerical precision for differential inclusions with uniqueness

Jérôme Bastien, Michelle Schatzman (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is 1/2 in general and 1 when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl's rheological model, our estimates in maximum norm do not depend on spatial dimension. ...

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