*Mathematical Methods in the Applied Sciences*Global weak solution to a generic reaction-diffusion nonlinear parabolic
system

We consider a new generic reaction-diffusion system, given as the
following form: ∂u/∂t - div(g(│(∇u_σ)│)∇u)=f(t,x,u,v,∇v), in Q_T ∂v/∂t
- d_v Δv=p(t,x,u,v,∇u), in Q_T u(0,.)=u_0, v(0,.)=v_0, in Ω (1)
∂u/∂η=0, ∂v/∂η=0, in ∑_T. Where Ω=]0,1[?×]0,1[, Q_T =]0,T
[? and T =]0,T [?, (T > 0), η is an outward normal to
domain Ω and u_0, v_0 is the image to be processed, x ∈Ω, σ
>0, ∇u_σ= u∗ ∇G_σ and G_σ= 1/√2πσ exp(-│x│^2/4σ). In
this study we are going to proof that there is a global weak solution to
the ptoblem (1), we truncate the system and show that it can be solved
by using Schauder fixed point theorem in Banach spaces. Finally by
making some estimations, we prove that the solution of the truncated
system converge to the solution of the problem.

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