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The BV solution of the parabolic equation with degeneracy on the boundary

100%

Zhan H., Chen S.

Open Mathematics

2016

tom 14

nr 1

272-282

Consider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

100%

Bialy M., Mironov A.

Open Mathematics

2012

tom 10

nr 5

1596-1604

We consider magnetic geodesic flows on the two-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a semi-Hamiltonian system of quasi-linear equations, i.e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.

Ograniczanie wyników

2 Open Mathematics

1 Bialy M.

1 Chen S.

1 Mironov A.

1 Zhan H.

1 2016

1 2012

Wyniki wyszukiwania

The BV solution of the parabolic equation with degeneracy on the boundary

New semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces