Displaying similar documents to “A new kind of the solution of degenerate parabolic equation with unbounded convection term”

Continuous dependence for BV-entropy solutions to strongly degenerate parabolic equations with variable coefficients

Watanabe, Hiroshi

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We consider the Cauchy problem for degenerate parabolic equations with variable coefficients. The equation has nonlinear convective term and degenerate diffusion term which depends on the spatial and time variables. In this paper, we prove the continuous dependence for entropy solutions in the space BV to the problem not only initial function but also all coefficients.

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.

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.

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...

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...

Maličky-Riečan's entropy as a version of operator entropy

Bartosz Frej (2006)

Fundamenta Mathematicae

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The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.

Entropy pairs of ℤ² and their directional properties

Kyewon Koh Park, Uijung Lee (2004)

Studia Mathematica

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Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.