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A new kind of the solution of degenerate parabolic equation with unbounded convection term

100%

Zhan H. Z.

Open Mathematics

2015

tom 13

nr 1

A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic equation [...] is introduced. If u0 ∈ L∞(RN), E = {Ei} ∈ (L2(QT))N and divE ∈ L2(QT), by a modified regularization method and choosing the suitable test functions, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained.

Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

88%

Ammar K.

Open Mathematics

2010

tom 8

nr 3

548-568

The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v 0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A 1, A 2,] with A 1 ≤ 0 ≤ A 2 so that the problem is of parabolic-hyperbolic type.

Ograniczanie wyników

2 Open Mathematics

1 Ammar K.

1 Zhan H. Z.

1 2015

1 2010

Wyniki wyszukiwania

A new kind of the solution of degenerate parabolic equation with unbounded convection term

Degenerate triply nonlinear problems with nonhomogeneous boundary conditions