Weak formulation with respect to time parameter.

n context of the condition ( Generic parabolic PDE setup ) we introduce the class For any , we apply the operation to the equation ( Generic parabolic PDE problem ) and integrate over : We integrate the first term by parts:

Problem

(Weak formulation with respect to time parameter) In context of the condition ( Generic parabolic PDE setup ) we seek such that

(Time-weak problem)

for any .