An Identification Problem for First-Order Degenerate Differential Equations

Identification problems for degenerate parabolic equations

“…Formulae (16) and (17) ensure that the multivalued linear operator A generates an infinitely differentiable semigroup on X (see [2]). Therefore, the reduced multivalued problem (5)- (7) possesses a unique strict solution (u, f ).…”

“…However, to the authors' knowledge, degenerate inverse problems for parabolic systems have not been studied thoroughly yet, even though this class of operators occurs in interesting theoretical and applied problems such as heat conduction processes, geophysics, controllability, oil search and underground filtration (see, e.g., [1], [2], [3] and [7], [8]). The main difficulties for these inverse problems come from the fact that the operators associated with the problem may have no bounded inverse and so the classical theory of semigroups does not apply.…”

Maximal time regularity for degenerate evolution integro-differential equations

“…Hence, it generates the semigroup {e t A } t≥0 satisfying (2.6). It is our purpose, here, to present some lemmas concerning the time regularity with respect to the norm of X of the convolution operators 1). In particular, we generalize to the case (α, β) = (1, 1) in (2.6) some results shown in [2] and [22] for the case (α, β) = (1, 1).…”

“…We refer to [1] for a possible application of Theorem 5.14 in the field of identification problems. Indeed, [1] is concerned with the problem of recovering the pair (v, h) in (5.23).…”

“…Indeed, [1] is concerned with the problem of recovering the pair (v, h) in (5.23). To this purpose, the first step is to consider (5.23) assuming h known, in order to find the suitable functional setting where to try to solve the problem, and then to use an additional given information to recover h in the correct functional space.…”