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

Watanabe, Hiroshi — 2017

Proceedings of Equadiff 14

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.

Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system

Hiroshi Watanabe;  Ken Shirakawa — 2014

Mathematica Bohemica

A one-dimensional version of a gradient system, known as “Kobayashi-Warren-Carter system”, is considered. In view of the difficulty of the uniqueness, we here set our goal to ensure a “stability” which comes out in the approximation approaches to the solutions. Based on this, the Main Theorem concludes that there is an admissible range of approximation differences, and in the scope of this range, any approximation method leads to a uniform type of solutions having a certain common features. Further,...

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