Chulalongkorn University Theses and Dissertations (Chula ETD)
Complete blow-up for a semilinear parabolic equation
Other Title (Parallel Title in Other Language of ETD)
การโบลว์อัพอย่างบริบูรณ์ของสมการเชิงพาราโบลากึ่งเชิงเส้น
Year (A.D.)
2003
Document Type
Thesis
First Advisor
Paisan Nakmahachalasint
Faculty/College
Faculty of Science (คณะวิทยาศาสตร์)
Degree Name
Master of Science
Degree Level
Master's Degree
Degree Discipline
Mathematics
DOI
10.58837/CHULA.THE.2003.1071
Abstract
Let T <= [infinity], a and x[subscript 0] be constants with a > 0 and 0 < x[subscript 0] < a. We establish the unique solution u for the following semilinear parabolic initial-boundary value problem: u[subscript t] (x,t)-u[subscript xx] (x,t) = [the integral of] (u(X[subscript 0],t)) for 0 < x < a, 0 < t < T, u(x,0) = [or {} is an empty set (x) >= 0 for 0 <= x <= a, u (0,t) = u[subscript x] (a,t) = 0 for 0 < t < T, Where [the integral of] and [or {} is an empty set] are given functions. We also show that under certain conditions, u blows up in a finite time, and the set of the blow-up points is the entire interval [0, a].
Other Abstract (Other language abstract of ETD)
กำหนด T <= [infinity], a และ x[subscript 0] เป็นค่าคงตัว โดยที่ a>0 และ 0
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Sawangtong, Panumart, "Complete blow-up for a semilinear parabolic equation" (2003). Chulalongkorn University Theses and Dissertations (Chula ETD). 56008.
https://digital.car.chula.ac.th/chulaetd/56008