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Parabolic equations involving 0th and 1st order terms with L1 data.

Thierry Goudon, Mazen Saad (2001)

Revista Matemática Iberoamericana

This paper is devoted to general parabolic equations involving 0th and 1st order terms, in linear and nonlinear expressions, while the data only belong to L1. Existence and entropic-uniqueness of solutions are proved.

Periodic parabolic problems with nonlinearities indefinite in sign.

Tomás Godoy, Uriel Kaufmann (2007)

Publicacions Matemàtiques

Let Ω ⊂ RN be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions a, b that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form Lu = λa (x, t) up - b (x, t) uq in Ω × R, where 0 < p, q < 1 and λ > 0. In some cases we also show the existence of solutions uλ in the interior of the positive cone and that uλ can...

Perona-Malik equation: properties of explicit finite volume scheme

Angela Handlovičová (2007)

Kybernetika

The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.

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