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Local existence for quasilinear parabolic systems under nonlinear boundary conditions. (English) Zbl 0655.35049
Summary: We prove local solvability of quasilinear parabolic systems by means of classical techniques based upon a priori estimates, without assuming any growth condition.

MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35B45 A priori estimates in context of PDEs
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