Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with partial-differential-equations
Search options not deleted
user 1003350
Questions on partial (as opposed to ordinary) differential equations - equations involving partial derivatives of one or more dependent variables with respect to more than one independent variables.
1
vote
2
answers
116
views
Verify the rarefaction wave solution of a general convex scalar problem
I am self-studying Numerical Methods for Conservation Laws by Leveque. I've been stuck on Exercise 3.7 for a while.
Question
Consider a general conservation law
$$
u_t+f(u)_x=0
$$
where $f(u)$ is conv …
- 349
3
votes
Verify the rarefaction wave solution of a general convex scalar problem
Split up the integral by considering the domain in $xt$ space. The figure below considers $f(u)=\frac{1}{2} u^2$.
The location of the rarefaction wave trailing edge is defined by $x=f'(u_l)t$, and th …
- 349
2
votes
Accepted
Show that the vanishing viscosity solution for $u_t+au_x=\epsilon u_{xx}$ is equal to $u_0(x...
Turns out I made a mistake evaluating the integration by parts! To solve this problem (from Leveque), I recommend following the procedure outlined in Strauss section 2.4.
Strauss develops the solution …
- 349
1
vote
1
answer
165
views
Show that the vanishing viscosity solution for $u_t+au_x=\epsilon u_{xx}$ is equal to $u_0(x...
I am self-studying Numerical Methods for Conservation Laws by Leveque.
Background
Leveque introduces the advection equation with constant speed $a$:
$$u_t+au_x=0$$
Given smooth initial data $u(x,0)=u_ …
- 349
3
votes
1
answer
216
views
What is the meaning of the wave equation characteristic lines?
Background
I am self-studying Introduction to PDEs by Walter Strauss. In chapter 1, Strauss describes that the characteristic lines of the PDE
$$
au_x+bu_t=0
$$
are given by $bx-at=C$, and the functio …
- 349
2
votes
Accepted
What is the meaning of the wave equation characteristic lines?
Mariano's comment pointed me in the right direction, I believe.
The characteristic lines are "lines on which information can move". So, when $x+ct=C$ is constant, $f(x+ct)$ is constant, but $g(x-ct)$ …
- 349
5
votes
0
answers
68
views
Derivation of entropy inequality for scalar conservation laws from viscous equation - discon...
I am self-studying Numerical Methods for Conservation Laws by LeVeque. I have a question about the derivation of the entropy inequality for the convex scalar conservation law
$$
u_t+f(u)_x=0\tag{1}
$$ …
- 349