| Abstrakt: |
We consider a scalar conservation law with source in a bounded open interval Ω ⊆ R . The equation arises from the macroscopic evolution of an interacting particle system. The source term models an external effort driving the solution to a given function ϱ with an intensity function V : Ω → R + that grows to infinity at ∂ Ω . We define the entropy solution u ∈ L ∞ and prove the uniqueness. When V is integrable, u satisfies the boundary conditions introduced by F. Otto (C. R. Acad. Sci. Paris, 322(1):729–734, 1996), which allows the solution to attain values at ∂ Ω different from the given boundary data. When the integral of V blows up, u satisfies an energy estimate and presents essential continuity at ∂ Ω in a weak sense. [ABSTRACT FROM AUTHOR] |
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