Obravnavamo difuzni proces v omrežju z neavtonomni Kirchhoffovi pogoji v vozliščih. Tudi difuzijski koeficienti so lahko odvisni od časa. Najprej z uporabo neavtonomnih bilinearnih form pokažemo ...obstoj in enoličnost rešitve. Glavni rezultati so obravnava dolgoročnega obnašanja rešitev. V primeru, ko se koeficienti prevodnosti in difuzije ujemajo (tako da se masa ohranja) pokažemo, da rešitev eksponentno konvergira k ravnovesju. Konvergenco rešitev pokažemo tudi še na nekaj durgih posebnih primerih.
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