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Global existence for the discrete diffusive coagulation-fragmentation equations in \(L^1\). (English) Zbl 1036.35089
This paper shows existence of global weak solutions to the discrete coagulation-fragmentation equations with diffusion: \[ \begin{cases} \partial_t c_i -d_i \triangle_xc_i =Q_i (c), &\text{ in } (0, \, + \infty) \times\Omega, \\ \partial_n c_i = 0, &\text{ on } (0, + \infty )\times \partial \Omega, \\ c(0) = c_i^{i_n}, &\text{ in } \Omega. \end{cases} \] Unlike previous works requiring \(L^{\infty}\)-estimates, an \(L^1\)-approach is developed in this paper. The authors show that under rather general assumptions on the kinetic coefficients, there exists at least a weak solution to the above equations for any initial datum \(c^{i_n}=(c_i^{i_n})_{i \geq 1}\) with finite total mass.

MSC:
35K57 Reaction-diffusion equations
82D60 Statistical mechanics of polymers
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
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