Asymptotic Almost Periodicity of Scalar Parabolic Equations with Almost Periodic Time Dependence
نویسندگان
چکیده
منابع مشابه
Asymptotic Almost Periodicity of Scalar Parabolic Equations with Almost Periodic Time Dependence
1 1. Introduction This paper is devoted to the study of asymptotic almost periodicity of bounded solutions for the following time almost periodic one dimensional scalar parabolic equation: u t = u xx + f (t, x, u, u x), t > 0, 0 < x < 1, u(t, 0) = u(t, 1) = 0, t > 0, (1.1) where f : IR 1 × [0, 1] × IR 1 × IR 1 → IR 1 is a C 2 function, and f (t, x, u, p) with all its partial derivatives (...
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The current paper is devoted to study of the asymptotic behavior of bounded solutions for the following type of parabolic equation: u t = u xx + f (t, x, u, u x), t > 0, 0 < x < 1, (1.1) with the boundary conditions: βu(t, 0) + (1 − β)u x (t, 0) = 0, βu(t, 1) + (1 − β)u x (t, 1) = 0, t > 0, (1.2) where β = 0 or 1, f : IR 1 × [0, 1] × IR 1 × IR 1 → IR 1 is C 2 , and f (t, x, u, p) with all its p...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1995
ISSN: 0022-0396
DOI: 10.1006/jdeq.1995.1152