Open AccessOn approximating initial data in some linear evolutionary equations involving fraction Laplacian
Author(s) -
Ramesh Karki
Publication year - 2022
Publication title -
mathematics in applied sciences and engineering
Language(s) - English
Resource type - Journals
ISSN - 2563-1926
DOI - 10.5206/mase/13511
Subject(s) - mathematics , sequence (biology) , geodetic datum , space (punctuation) , laplace operator , dirichlet distribution , boundary (topology) , dirichlet boundary condition , linear equation , pure mathematics , boundary value problem , mathematical analysis , computer science , genetics , cartography , biology , geography , operating system
We study an inverse problem of recovering the intial datum in a one-dimensional linear equation with Dirichlet boundary conditions when finitely many values (samples) of the solution at a suitably fixed space loaction and suitably chosen finitely many later time instances are known. More specifically, we do this. We consider a one-dimentional linear evolutionary equation invliing a Dirichlet fractional Laplacian and the unknown intial datum f that is assumed to be in a suitable subset of a Sovolev space. Then we investigate how to construct a sequence of future times and choose n so that from n samples taken at a suitably fixed space location and the first n terms of the time sequence we can constrcut an approximation to f with the desired accuracy.