Abstract
The paper deals with non-classical initial-boundary value problems for parabolic equations with a fractional Laplacian. We study the existence and uniqueness of a mild solution to our problem. The continuous dependence of the solution on the given data is shown and the ill-posedness of the mild solution at t = 0 is also considered. In order to avoid such ill-posedness, we construct a regularized solution using the Fourier truncation method. An error estimate and the convergence rate between the regularized solution and the exact solution are obtained.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.