Decreasing of the L^1 norm and mass conservation for Porous Medium Equations with advection
In this paper, we show that the $L^1$ norm of the bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form u_t + div f(x,t,u) = div(|u|^{\alpha}\nabla u), x \in R^n , t > 0, where \alpha > 0 is constant, decrease, under fairly broad conditions in...
| Main Authors: | , |
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| Format: | Article |
| Language: | Portuguese |
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Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)
2018-12-01
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| Series: | REMAT |
| Subjects: | |
| Online Access: | https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/2959 |
| Summary: | In this paper, we show that the $L^1$ norm of the bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form
u_t + div f(x,t,u) = div(|u|^{\alpha}\nabla u), x \in R^n , t > 0,
where \alpha > 0 is constant, decrease, under fairly broad conditions in advection flow f. In addition, we derive the mass conservation property for positive (or negative) solutions. |
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| ISSN: | 2447-2689 |