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The mathematical term well-posed problem (Hadamard well-posed) is defined that mathematical platforms of physical phenomena should have the following properties: (i) A solution exists.
Then, for every (nu_{1}, nu_{2} in mathbb {R}), there exists a function (u in C^{1}(I)) with (A_{u} cdot(Phicirc u')in W^{1,1}(I)), a solution of problem (5).
Then Neumann problem (1.1), (1.4) has a solution u ∈ W ( I ) such that α ( t ) ≤ u ( t ) ≤ β ( t ) for every t ∈ I. Proof Proposition 5.2 insures the existence of u ∈ W ( I ), a solution of (5.1 λ ) for λ = 1.
Then Dirichlet problem (1.1), (1.2) has a solution u ∈ W ( I ) such that α ( t ) ≤ u ( t ) ≤ β ( t ) for every t ∈ I. Proof Proposition 3.2 insures the existence of u ∈ W ( I ), a solution of (3.1 λ ) for λ = 1.
Then periodic problem (1.1), (1.3) has a solution u ∈ W ( I ) such that α ( t ) ≤ u ( t ) ≤ β ( t ) for every t ∈ I. Proof Proposition 4.2 insures the existence of u ∈ W ( I ), a solution of (4.1 λ ) for λ = 1.
Model system I, a solution of 10 µM (0.1%) amyloglucosidase and 340 µM (0.5%) lysozyme, 10 mM hydrogencarbonate and 5 mM di-hydrogenphosphate (Fig. 1 curve d, 5A curve b, 5B curve b) was found to have a buffer power of 158 µmol (H+) and 38 µmol of base.
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But I think I have a solution.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com