id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-461	Floridia, Giuseppe	Nonnegative controllability for a class of nonlinear degenerate parabolic equations with application to climate science	2020	27	.pdf	application/pdf	11812	622	69	Integrating by parts, recalling that u−(·, t) ∈ H1 a(−1, 1) for every t ∈ (0, T ),and using Proposition 3.1 we deduce∫ 1 −1 (a(x)ux)xu − dx = [a(x)uxu −]1−1 − ∫ 1 −1 a(x)ux(u−)x dx = [a(x)uxu −]1−1 + ∫ 1 −1 a(x)u2x dx . (3.2) If β1γ1 6= 0, keeping in mind the boundary conditions, for t ∈ (0, T ) we have [a(x)uxu −]1−1 = a(1)ux(1, t)u−(1, t)− a(−1)ux(−1, t)u−(−1, t) = −γ0 γ1 (u+(1, t)− u−(1, t))u−(1, t) For a.e. x ∈ (−1, 1), from the equation ut(·, t) = αεj(·) T − T1 u(·, t) + ((a(·)ux(·, t))x + f(·, t, u)) t ∈ (T1, T ), by the classical variation constants technique, we obtain a representation formula of the solution u(x, t) of (3.24), that computed at time T , for x ∈ (−1, 1), becomes u(x, T )	cache/ejde-461.pdf	txt/ejde-461.txt