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Global solutions for quasilinear parabolic systems. (English) Zbl 1043.35066

An approach is presented for proving the global existence of classical solutions of the quasilinear parabolic systems like \[ u_t-\text{ div}(a(t,x,u,v)\nabla u)=f(t,u,v,\nabla u), \quad t>0, \]
\[ v_t-\alpha\,\text{ div}(b(t,x,v)\nabla v)=g(t,u,v,\alpha\nabla v), \quad t>0, \] with homogeneous Dirichlet boundary condition in bounded domain with smooth boundary.

MSC:

35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
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