arXiv
Open Access
2015
Stochastic Allen-Cahn equation with mobility
Lorenzo Bertini
Paolo Buttà
Adriano Pisante
Abstrak
We introduce a class of stochastic Allen-Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the $d$-dimensional torus in the time interval $[0,T]$. Assuming that $d\le 3$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process $u$ in $L^2$ with continuous paths, satisfying almost surely the regularity properties $u\in C([0,T]; H^1)$ and $u\in L^2([0,T];H^2)$.
Penulis (3)
L
Lorenzo Bertini
P
Paolo Buttà
A
Adriano Pisante
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2015
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓