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\(\Gamma\)-convergence and non local effect: A non-linear case. (English) Zbl 0892.35020
Cioranescu, Doina (ed.) et al., Homogenization and applications to material sciences. Proceedings of the international conference, Nice, France, June 6–10, 1995. Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl. 9, 279-290 (1995).
Summary: We characterize, in terms of the Young measures of the sequence \(a_\varepsilon\), the weak sequential \(\Gamma\)-limit of the functionals \(J_\varepsilon (v)\), associated to the nonlinear equation \[ \partial_t u_\varepsilon (t,x)+ a_\varepsilon (x)g \bigl( u_\varepsilon (t,x)\bigr) = f,\quad u_\varepsilon (0,x)=u_0. \] The non-additivity of the limit functional \(J(v)\) may be seen as a consequence of the nonlocal effect, similar to the one that occurs in the linear case.
For the entire collection see [Zbl 0873.00028].

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs