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A degenerate parabolic system for three-phase flows in porous media

Vladimir Shelukhin (2007)

Annales mathématiques Blaise Pascal

A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data.

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

Huashui Zhan (2015)

Open Mathematics

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.

A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.

J. I. Díaz, L. Tello (1999)

Collectanea Mathematica

We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a...

A parabolic quasilinear problem for linear growth functionals.

Fuensanta Andreu, Vincent Caselles, José María Mazón (2002)

Revista Matemática Iberoamericana

We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth.

A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations

Mario Ohlberger (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation c t + · ( 𝐮 f ( c ) ) - · ( D c ) + λ c = 0 . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L 1 -norm, independent of the diffusion parameter D . The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...

A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations

Mario Ohlberger (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation c t + · ( 𝐮 f ( c ) ) - · ( D c ) + λ c = 0 . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L1-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...

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