Differential and Integral Equations

Stochastic variational inequalities for a wave equation

Jong Uhn Kim

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Abstract

We discuss evolution variational inequalities for a wave equation with unilateral constraint on the velocity. Both deterministic and stochastic obstacle problems will be considered. For deterministic obstacles, we will focus on the case which is directly related to stochastic equations. This makes it necessary to formulate a new definition of a solution. Based on this definition, we will establish existence and uniqueness of a solution to both deterministic and stochastic problems.

Article information

Source
Differential Integral Equations Volume 29, Number 1/2 (2016), 93-126.

Dates
First available in Project Euclid: 24 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1448323254

Mathematical Reviews number (MathSciNet)
MR3450750

Zentralblatt MATH identifier
1349.35250

Subjects
Primary: 35L85: Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H15: Stochastic partial differential equations [See also 35R60]

Citation

Kim, Jong Uhn. Stochastic variational inequalities for a wave equation. Differential Integral Equations 29 (2016), no. 1/2, 93--126. https://projecteuclid.org/euclid.die/1448323254.


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