科研之友
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摘要
By combining the formalism of [8] with a discrete approach close to the considerations of [6], we interpret and we solve the rough partial differential equation dy(t) = Ay(t) dt + Sigma(m)(i=1) f(i)(y(t)) dx(t)(i) (t epsilon [0,T]) on a compact domain O of R-n, where A is a rather general elliptic operator of L-p (O) (p > 1), f(i)(phi)(xi) : = f(i) (phi(xi)) and x is the generator of a 2-rough path. The (global) existence, uniqueness and continuity of a solution is established under classical regularity assumptions for fi. Some identification procedures are also provided in order to justify our interpretation of the problem.
- 出版日期2011-8-19
