همواری جوابهای یک معادله پخش-واکنش در محیط متخلخل ناهمگن

نوع مقاله : مقاله پژوهشی

نویسنده

گروه ریاضی دانشگاه صنعتی شریف

چکیده

در این مقاله نظم جواب معادله پخش-واکنش $\Delta u(x) = |u(x)|^{\gamma(x)-1} u(x) $ را مورد مطالعه قرار می‌دهیم. این معادله برای مدلسازی پخش گاز در یک محیط کاتالیزور متخلخل ناهمگن به کار می‌رود و توان $\gamma(x)$ می‌تواند تابعی ناپیوسته باشد. به طور خاص مرتبه کاهش جواب در نزدیکی سطح تراز $\{u=0\}$ مورد بررسی قرار می‌دهیم.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Regularity of a Reaction-Diffusion Equation in Inhomogeneous Porous Media

نویسنده [English]

  • Morteza Fotouhi
Sharif University of Technology
چکیده [English]

In this paper, we study the reaction-diffusion equation $\Delta u(x) = |u(x)|^{\gamma(x)-1} u(x) $ from a regularity point of view. This equation is used for modelling the distribution of a gas in an inhomogeneous porous catalyst. And the power $\gamma(x)$ can be a discontinuous function. In particular, we study the vanishing order of solution near the zero level set $\{u=0\}$.

کلیدواژه‌ها [English]

  • Reaction-Diffusion Equations
  • Regularity of solution
  • Vanishing order of solution
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