A Viability Result for Semilinear Reaction-Diffusion Systems

Viability for nonlinear multi-valued reaction–diffusion systems

“…The viability problem for reaction-diffusion systems of the form (1.1) was studied by Burlicȃ-Roşu [8,9], where A and B are linear operators, generators of two C 0 -semigroups and F, G are single-valued, continuous functions such that A + F and/or B + G are locally of β-compact type. Necula-Vrabie [19] considered the case in which A and B are nonlinear, m-dissipative operators, B generates a compact semigroup, F, G are single-valued, continuous functions and F : R × X × Y → X is locally Lipschitz with respect to its second argument.…”

The existence and uniqueness of integral solutions to some nonlinear reaction–diffusion system with nonlocal retarded initial conditions

“…(1) Here, τ 0 = 0 ≤ τ 1 ≤ τ 2 ≤ · · · ≤ τ n = τ to be fixed, f : The system (1) has been addressed by several authors, and they analyzed various cases, such as Alam and Alam [1], Burlică [2], Burlică and Roşu [3][4][5], Diaz and Vrabie [6], Meknani and Zhang [7], Neucala and Vrabie [8], Roşu [9,10] been studied by Burlică and Roşu [11], Vrabie [12][13][14] , Garcia and Reich [15] and Paicu and Vrabie [31]. Otherwise, the result for nonlinear evolution inclusions with nonlocal retarded initial conditions was investigated by Vrabie [16] and references therein.…”

Nonlinear delay reaction-diffusion systems with nonlocal initial conditions having affine growth

“…For parabolic systems with nonlinear, nonlocal initial conditions we mention the paper of Infante and Maciejewski [24]. Concerning the reaction-diffusion systems without delay see: Burlicȃ [8], Burlicȃ and Roşu [9], [10], Díaz and Vrabie [19], Necula and Vrabie [30], Roşu [33], [34]. Existence results for reaction-diffusion systems with delay and nonlocal initial conditions were obtained in Burlicȃ, Roşu and Vrabie [14] for the single-valued case and by Burlicȃ and Roşu [12] for the multi-valued case.…”