Abstract
The existence of nonnegative weak solutions globally in time of a nonlinear fourth-order parabolic equation in one space dimension is shown. This equation arises in the study of interface fluctuations in spin systems and in quantum semiconductor modeling. The problem is considered on a bounded interval subject to initial and Dirichlet and Neumann boundary conditions. Further, the initial datum is assumed only to be nonnegative and to satisfy a weak integrability condition. The main difficulty of the existence proof is to ensure that the solutions stay nonnegative and exist globally in time. The first property is obtained by an exponential transformation of variables. Moreover, entropy-type estimates allow for the proof of the second property. Results concerning the regularity and long-time behavior are given. Finally, numerical experiments underlining the preservation of positivity are presented.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
