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Results tagged with hyperbolic-pde
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user 117762
Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
2
votes
0
answers
83
views
Changing a little assumptions in famous paper Vanishing viscosity solutions of nonlinear hyp...
The question that I hope to find some answer here is: do the results from
Bianchini, Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems, 2005
paper still apply if we change a littl …
- 6,367
1
vote
2
answers
244
views
Transformation from the PDE problem with a source to the PDE problem without it and viceversa
In the study of nonlinear conservation laws a lot of time I work on the two problems given bellow:
$$(1) \hspace{1cm} \begin{cases}
u_t+(f_{1}(u))_x=\lambda \cdot g(u) \\[2ex]
u(x,0)=h_{1}(x)
\en …
- 108k
7
votes
1
answer
865
views
Comparing weak and strong solutions of a PDE problems
A few days ago I was reading the paper:
"Relative entropies, suitable weak solutions, and weak-strong uniqueness for the compressible Navier-Stokes system" - Feireisl, Jin, Novotny, 2012 [Arxiv].
…
- 5,380
1
vote
0
answers
159
views
Reference request for a paper with Vanishing viscosity method and smooth approximation of in...
I am trying to find the papers/books/notes that study problem (1),(3) given bellow using the vanishing viscosity method. I am especially interested in solutions in Sobolev spaces.
More detailed expl …
- 657
1
vote
2
answers
369
views
Banach space-valued test functions in the definition of a weak solution of a PDE problem
In the literature about PDEs it is easy to find books that talk about weak solutions of a partial differential equations. A short reminder of the usual definition is given bellow. More information cou …
- 778
2
votes
0
answers
90
views
Approximation of deterministic problems in the PDEs with the stochastic ones
A lot of problems in PDE theory are solved in the following way:
The original problem is quite hard and we can't solve it, so we make the approximation problem that we can solve. Than we go back and w …
- 657
3
votes
2
answers
920
views
Method of characteristics for 2x2 systems
In the literature it is easy to find books that show, step by step, how to get the solution of partial differential equation using various techniques, but it is not so easy to do the same for PDE syst …
- 52.3k
3
votes
0
answers
198
views
Reference request on connection between PDE problems
I am trying to find references in the literature that connect solutions of any two of the problems given bellow. I study deterministic and stochastic conservation laws. Problems that I am interested i …
- 657
4
votes
0
answers
94
views
Reference request on theory about Stochastic Riemann problem
I am trying to find references in the literature that deal with the Stochastic Riemann problem. Let me explain it a bit.
On one hand, in the literature it is not hard to find books or papers that deal …
- 657
1
vote
0
answers
888
views
Different types of a test functions in weak solutions of a PDEs
In the literature about PDEs it is easy to find books that talk about weak solutions of a partial differential equations. A short reminder of the most usual definition is given bellow.
Let's conside …
- 4,713