Displaying similar documents to “A continuous version of the Filippov-Gronwall inequality for differential inclusions”

Layering methods for nonlinear partial differential equations of first order

Avron Douglis (1972)

Annales de l'institut Fourier

Similarity:

This paper is concerned with generalized, discontinuous solutions of initial value problems for nonlinear first order partial differential equations. “Layering” is a method of approximating an arbitrary generalized solution by dividing its domain, say a half-space t ≥ 0 , into thin layers ( i - ℓ ) h ≤ t ≤ i h , i = 1 , 2 , ... ( h > 0 ) , and using a strict solution u i in the i -th layer. On the interface t = ( i - ℓ ) h , u t is required to reduce to a smooth function approximating the values on that plane of u i - ℓ . The resulting stratified configuration...