Abstract
We consider a first boundary-value problem in a quadrant of the plane for a second-order linear parabolic equation with two independent variables. The boundary function may increase along with the time variable. We show that the solution remains bounded at interior points when the highest-order coefficient decreases sufficiently rapidly or when the lowest order coefficients, having appropriate signs, increase sufficiently rapidly. Similar results are established for certain quasilinear nonuniformly parabolic equations. Examples are constructed showing the accuracy of the results obtained.
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.
