Correctness investigation of a boundary value problem for a parabolic equation with nonlocal space operator with respect to the solution gradient

11th International Conference on "Mesh methods for boundary-value problems and applications"

Ivanova, A.S.^1 ; Pavlova, M.F.^1

Department of Computational Mathematics, Institute of Computational Mathematics and Information Technologies, Kazan Federal University, 18 Kremlyovskaya Street, Kazan

420008, Russia^1

关键词: Bounded function;    Existence and uniqueness;    Nonlocal;    Parabolic Equations;    Space operators;    Strongly-monotones;    Vector-valued function;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012044/pdf
DOI  :  10.1088/1757-899X/158/1/012044

来源: IOP

【 摘 要 】

We consider the parabolic equation whose space operator is product of nonlinear bounded function which depends on nonlocal characteristic with respect to a solution gradient and strongly monotone, potential operator. The existence and uniqueness of the solution in the class of the vector-valued functions with values in Sobolev space are proved.