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Displaying similar documents to “Continuous dependence for BV-entropy solutions to strongly degenerate parabolic equations with variable coefficients”

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

Huashui Zhan (2015)

Open Mathematics

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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.

Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems

Philippe Laurençot, Bogdan-Vasile Matioc (2023)

Archivum Mathematicum

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Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown to coincide with the unique strong solution determined by the same initial condition on the maximal existence interval of the latter. The proof relies on an estimate established for a relative entropy associated to the system.

Cross-Diffusion Systems with Entropy Structure

Jüngel, Ansgar

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Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on local-in-time existence results for general systems with normally elliptic diffusion operators, due to Amann, and global-in-time existence theorems by Lepoutre, Moussa, and co-workers for cross-diffusion systems with an additional Laplace structure. The boundedness-by-entropy method allows for global bounded weak solutions to certain diffusion systems. Furthermore, a partial result on the uniqueness...

Continuous dependence of the entropy solution of general parabolic equation

Mohamed Maliki (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider the general parabolic equation : u t - Δ b ( u ) + d i v F ( u ) = f in Q = ] 0 , T [ × ℝ N , T > 0 with u 0 ∈ L ∞ ( ℝ N ) , for a . e t ∈ ] 0 , T [ , f ( t ) ∈ L ∞ ( ℝ N ) and ∫ 0 T f ( t ) L ∞ ( ℝ N ) d t < ∞ . We prove the continuous dependence of the entropy solution with respect to F , b , f and the initial data u 0 of the associated Cauchy problem. This type of solution was introduced and studied in [MT3]. We start by recalling the definition of weak solution and entropy solution. By applying an abstract result (Theorem...

Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

Kaouther Ammar (2010)

Open Mathematics

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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.