Convergence to Steady States of Solutions of Non-autonomous Heat Equations in $$\mathbb{R}^{N}$$

Springer Science and Business Media LLC - Tập 19 Số 3 - Trang 777-788 - 2007
Chill, R.1, Jendoubi, M. A.2
1Laboratoire de Mathématiques et Applications de Metz et CNRS, Université Paul Verlaine – Metz, Metz Cedex 1, France
2Département de Mathématiques, Faculté des Sciences de Bizerte, Jarzouna Bizerte, Tunisie

Tóm tắt

Under certain assumptions on f and g we prove that positive, global and bounded solutions u of the non-autonomous heat equation $$ u_t - \Delta u + f(u) = g(t,x)$$ in $$\mathbb{R}^{N}$$ (N ≥ 3) converge to a steady state.

Tài liệu tham khảo

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