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I'm aware that there are a lot of counterexamples to show that distributional solutions for hyperbolic (scalar) conservation laws are not unique.

However, I'd like to ask:

  1. Conceptually, at which point of a proof of uniqueness is the definition of distributional solution not enough to go on?

    Conceptually, at which point of a proof of uniqueness is the definition of distributional solution not enough to go on?

  2. Why is the definition of entropy solution useful in the proof of uniqueness for hyperbolic conservation laws?

  1. Why is the definition of entropy solution useful in the proof of uniqueness for hyperbolic conservation laws?

I'm aware that there are a lot of counterexamples to show that distributional solutions for hyperbolic (scalar) conservation laws are not unique.

However, I'd like to ask:

  1. Conceptually, at which point of a proof of uniqueness is the definition of distributional solution not enough to go on?
  1. Why is the definition of entropy solution useful in the proof of uniqueness for hyperbolic conservation laws?

I'm aware that there are a lot of counterexamples to show that distributional solutions for hyperbolic (scalar) conservation laws are not unique.

However, I'd like to ask:

  1. Conceptually, at which point of a proof of uniqueness is the definition of distributional solution not enough to go on?

  2. Why is the definition of entropy solution useful in the proof of uniqueness for hyperbolic conservation laws?

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user60665
user60665

Why is the definition of entropy solution necessary to prove uniqueness for hyperbolic conservation laws?

I'm aware that there are a lot of counterexamples to show that distributional solutions for hyperbolic (scalar) conservation laws are not unique.

However, I'd like to ask:

  1. Conceptually, at which point of a proof of uniqueness is the definition of distributional solution not enough to go on?
  1. Why is the definition of entropy solution useful in the proof of uniqueness for hyperbolic conservation laws?