Loading...
Initial-boundary value problems for a reaction-diffusion equation
Himonas, A. Alexandrou Mantzavinos, Dionyssios Yan, Fangchi
Himonas, A. Alexandrou
Mantzavinos, Dionyssios
Yan, Fangchi
Citations
Altmetric:
Abstract
A novel approach that utilizes Fokas’s unified transform is employed for studying a reaction-diffusion equation with power nonlinearity formulated either on the half-line or on a finite interval with data in Sobolev spaces. This approach was recently introduced for initial-boundary value problems involving dispersive nonlinear equations such as the nonlinear Schrödinger and the Korteweg-de Vries equations. Thus, the present work extends the new approach from dispersive equations to diffusive ones, demonstrating the universality of the unified transform in the analysis of nonlinear evolution equations on domains with a boundary.
Description
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Math. Phys. 60, 081509 (2019); doi: 10.1063/1.5118767 and may be found at https://aip.scitation.org/doi/10.1063/1.5118767.
Date
2019-08-27
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Physics
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
Citation
A. Alexandrou Himonas, Dionyssios Mantzavinos, and Fangchi Yan , "Initial-boundary value problems for a reaction-diffusion equation", Journal of Mathematical Physics 60, 081509 (2019) https://doi.org/10.1063/1.5118767