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Results tagged with conservation-laws
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user 61771
1
vote
Comparing solutions of PDE problem with different initial conditions
I'm not sure this really qualifies as an answer (there's not much here beyond notation really), but one general way of thinking about this sort of problem is as follows. Sorry if any of this seems a b …
- 778
2
votes
Accepted
Banach space-valued test functions in the definition of a weak solution of a PDE problem
Writing your equation (3) as $a(u,\psi)=0$, it is indeed common to call $u\in L^1_\mathrm{loc}$ a `weak solution' to your problem if and only it satisfies
$$
a(u,\psi) = 0 \mbox{ for all } \psi \in …
- 778