Differential and Integral Equations

On a class of implicit evolution variational inequalities

Pierluigi Colli and Giuseppe Savaré

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The initial value problem is studied for a parabolic variational inequality where the constraints are imposed on the time derivative of the solution and with a nonlinear right hand side. The existence of a solution is established under rather general conditions on the nonlinearity, while uniqueness and regularity properties are deduced in a more restrictive setting. An approximation via finite differences in time is presented and convergence results along with error estimates are proved. Applications of the model problem are given in the framework of nonlinear partial differential equations and systems.

Article information

Differential Integral Equations, Volume 8, Number 8 (1995), 2097-2124.

First available in Project Euclid: 20 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 35K85: Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40] 49J40: Variational methods including variational inequalities [See also 47J20]


Colli, Pierluigi; Savaré, Giuseppe. On a class of implicit evolution variational inequalities. Differential Integral Equations 8 (1995), no. 8, 2097--2124. https://projecteuclid.org/euclid.die/1369056142

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