I suggest you have a look at:
Also, to me it seems like your problem is linear and Im not certain that your problem is coercive, see for instance: https://www.math.tamu.edu/~guermond/M610_SPRING_2005/lect3.pdf
I suggest you have a look at:
Also, to me it seems like your problem is linear and Im not certain that your problem is coercive, see for instance: https://www.math.tamu.edu/~guermond/M610_SPRING_2005/lect3.pdf