| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 100 | |
| Number of page(s) | 22 | |
| DOI | https://doi.org/10.1051/cocv/2020028 | |
| Published online | 10 December 2020 | |
Stochastic optimal control of a evolutionary p-Laplace equation with multiplicative Lévy noise
Department of Mathematics, Indian Institute of Technology Delhi,
Hauz Khas,
New Delhi
110016, India.
* Corresponding author: majee@maths.iitd.ac.in
Received:
12
June
2019
Accepted:
11
May
2020
In this article, we are interested in an initial value optimal control problem for a evolutionary p-Laplace equation driven by multiplicative Lévy noise. We first present wellposedness of a weak solution by using an implicit time discretization of the problem, along with the Jakubowski version of the Skorokhod theorem for a non-metric space. We then formulate associated control problem, and establish existence of an optimal solution by using variational method and exploiting the convexity property of the cost functional.
Mathematics Subject Classification: 45K05 / 46S50 / 49L20 / 49L25 / 91A23 / 93E20
Key words: Evolutionary p-Laplace equation / stochastic PDEs / weak solution / Skorokhod theorem
© EDP Sciences, SMAI 2020
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