Note on chemical interfacial reaction models
From the authors' introduction. We consider the following parabolic system with nonlinear boundary conditions. Find \(u_ i=u_ i(x,t)\) \((i=1,2,3)\) satisfying \[ (1)\quad a_ i(x)\partial u_ i/\partial t=\partial^ 2u_ i/\partial x^ 2,\quad x\in I\equiv (0,1),\quad t\in (0,\infty), \] (2) \((\partial u_ i/\partial x)(0,t)=R_ i(u_ 1(0,t)\), \(u_ 2(0,t)\), \(u_ 3(0,t))\), \(t\in (0,\infty)\), (3) \((\partial u_ i/\partial x)(1,t)=0\), \(t\in (0,\infty)\), (4) \(u_ i(x,0)=\phi_ i(x)\), \(x\in I\), where \(a_ i\) and \(R_ i\) \((i=1,2,3)\) are given functions and \(\phi_ i\) \((i=1,2,3)\) are given initial data.
scientific article; zbMATH DE number 4023868