Toronto Math Forum
APM346-2023S => APM346--Lectures & Home Assignments => Chapter 10 => Topic started by: Issra on April 01, 2023, 07:31:40 AM
-
Posted here since there is no section for Chapter 10.
In Lemma 1 in S10.1 (http://www.math.toronto.edu/ivrii/PDE-textbook/Chapter10/S10.1.html#:~:text=Lemma%201.,.%20Contradiction!), why is the condition $\phi(t_0) = \phi(t_1) = 0 $ necessary?
-
This condition is not necessary. However more conditions to $\phi$ lead to a lesser class of admissible $\phi$ in the assumption and thus to weaker assumption of Lemma 1, and thus to stronger and more general statement.