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Abstract: This Note is devoted to the analysis of the null controllability of a nonlinear reaction–diffusion system, approximating a parabolic–elliptic system, modeling electrical activity in the heart. The uniform, with respect to the degenerating parameter, null controllability of the approximating system by a single control force acting on a subdomain is shown. The proof needs a precise estimate with respect to the degenerating parameter and it is done combining Carleman estimates and energy inequalities. [Copyright &y& Elsevier]

Abstract: We define renormalized solutions for the problems of the kind in , . Here β is a maximal monotone graph in , and , , is the fractional Laplace operator which is a particular case of Lévy diffusions. We prove well-posedness in the framework of renormalized solutions. Then the Cauchy problem for the associated evolution equations can be solved using the Crandall–Liggett semigroup technique. [ABSTRACT FROM AUTHOR]