Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Help me please to solve this equation: $u_{t}+c\left [ u(1-u) \right ]_{x}=0$ in [a,b]

$c$ is constant. Find smooth boundary and initial conditions when the solution is discontinuous .

Thanks a lot!

share|cite|improve this question
On which domain do you consider your equation? Is there any correspondance between $q$ and $u$? Is $c$ constant? – martini Jul 18 '12 at 10:23
@martini Oh, thanks. It's no q just u, in[a,b], and indeed c is constant – Lilly Jul 18 '12 at 10:40
Does the expanded form of your PDE is $u_t+cu_x-2cuu_x=0$ ? – doraemonpaul Jul 18 '12 at 21:19
@doraemonpaul yes, it's the expand form – Lilly Jul 22 '12 at 8:44
up vote 1 down vote accepted





This belongs to a PDE of the form

So the general solution is $x=ct(1-2u)+C(u)$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.