In this paper,the existence theorem for a quasi solution of an inverse fractional stochastic parabolic equation driven by multiplicative noise in the form cD_(t)^(a)u-div(g(x,▽u))=f(x,u)+σ(x,u)w(t)is given.In this e...In this paper,the existence theorem for a quasi solution of an inverse fractional stochastic parabolic equation driven by multiplicative noise in the form cD_(t)^(a)u-div(g(x,▽u))=f(x,u)+σ(x,u)w(t)is given.In this equation,the fractional derivative is considered in the Caputo sense.Also,the random function g is unknown and should be determined.To identify the unknown coefficient,the minimization and stochastic variational formulation methods in a fractional stochastic Sobolev space are used.Indeed,we obtain a stability estimation and then prove the continuity of the minimization functional using obtained stability estimation.These results show the existence of the quasi solution for the mentioned problem.展开更多
文摘In this paper,the existence theorem for a quasi solution of an inverse fractional stochastic parabolic equation driven by multiplicative noise in the form cD_(t)^(a)u-div(g(x,▽u))=f(x,u)+σ(x,u)w(t)is given.In this equation,the fractional derivative is considered in the Caputo sense.Also,the random function g is unknown and should be determined.To identify the unknown coefficient,the minimization and stochastic variational formulation methods in a fractional stochastic Sobolev space are used.Indeed,we obtain a stability estimation and then prove the continuity of the minimization functional using obtained stability estimation.These results show the existence of the quasi solution for the mentioned problem.
