Abstract
We consider the following inverse problem of finding the pair (u, p) which satisfies the following: u1 = uxx + p(t)u + F(x, t, u, ux, p(t), 0 < x < 1, 0 < t ≤ T; u(x,0) = u0(x), 0 < x < 1, ux(0, t) = f(t), ux(1, t) = g(t), 0 < t ≤ T; and ∝01ψ(x,t) u(x, t)dx = E(t), 0 < t ≤ T; where u0, f, g, F, ψ, and E are known functions. The existence, uniqueness, regularity, and the continuous dependence of the solution upon the data are demonstrated.
Original language | English |
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Pages (from-to) | 470-484 |
Number of pages | 15 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 145 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Jan 1990 |
Externally published | Yes |
ASJC Scopus subject areas
- Analysis
- Applied Mathematics