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Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

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]. …
Mark's user avatar
  • 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 …
Mark's user avatar
  • 657
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 …
Mark's user avatar
  • 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 …
Mark's user avatar
  • 657
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 …
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  • 657
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 …
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  • 657
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 …
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  • 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 …
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  • 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 …
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  • 657
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 …
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  • 657