New global Carleman estimates and null controllability for a stochastic Cahn-Hilliard type equation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909280891830272 |
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| author | Zhang, Sen Gao, Hang Yuan, Ganghua |
| author_facet | Zhang, Sen Gao, Hang Yuan, Ganghua |
| contents | In this paper, we study the null controllability for a stochastic semilinear CahnHilliard type equation, whose semilinear term contains first and second order derivatives of solutions. To start with, an improved global Carleman estimate for linear backward stochastic fourth order parabolic equations with $L^2$-valued source terms is derived, which is based on a new fundamental identity for a stochastic fourth order parabolic operator. Based on it, we establish a new global Carleman estimate for linear backward stochastic fourth order parabolic equations with $H^{-2}$-valued source terms, which, together with a fixed point argument, derive the desired null controllability for the stochastic Cahn-Hilliard type equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New global Carleman estimates and null controllability for a stochastic Cahn-Hilliard type equation Zhang, Sen Gao, Hang Yuan, Ganghua Optimization and Control Analysis of PDEs In this paper, we study the null controllability for a stochastic semilinear CahnHilliard type equation, whose semilinear term contains first and second order derivatives of solutions. To start with, an improved global Carleman estimate for linear backward stochastic fourth order parabolic equations with $L^2$-valued source terms is derived, which is based on a new fundamental identity for a stochastic fourth order parabolic operator. Based on it, we establish a new global Carleman estimate for linear backward stochastic fourth order parabolic equations with $H^{-2}$-valued source terms, which, together with a fixed point argument, derive the desired null controllability for the stochastic Cahn-Hilliard type equation. |
| title | New global Carleman estimates and null controllability for a stochastic Cahn-Hilliard type equation |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2408.03517 |