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Uniqueness of solutions to an Abel type nonlinear integral equation on the half line

100%

Mydlarczyk W.

Open Mathematics

2012

tom 10

nr 6

1995-2002

We consider a convolution-type integral equation u = k ⋆ g(u) on the half line (−∞; a), a ∈ ℝ, with kernel k(x) = x α−1, 0 < α, and function g(u), continuous and nondecreasing, such that g(0) = 0 and 0 < g(u) for 0 < u. We concentrate on the uniqueness problem for this equation, and we prove that if α ∈ (1, 4), then for any two nontrivial solutions u 1, u 2 there exists a constant c ∈ ℝ such that u 2(x) = u 1(x +c), −∞ < x. The results are obtained by applying Hilbert projective metrics.

Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids

84%

Bárta T.

Open Mathematics

2013

tom 11

nr 6

1112-1128

We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times. The example we have in mind foremost are materials with memory.

Ograniczanie wyników

2 Open Mathematics

1 Bárta T.

1 Mydlarczyk W.

1 2013

1 2012

Wyniki wyszukiwania

Uniqueness of solutions to an Abel type nonlinear integral equation on the half line

Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids