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Global existence for semilinear parabolic systems. (English) Zbl 0564.35060
This paper studies the problem of global existence for strongly coupled semilinear parabolic systems of arbitrary even order under linear time- dependent boundary conditions. In particular it is shown that there exist classical global solutions provided the nonlinearity satisfies appropriate polynomial growth restrictions and a priori estimates in some weak norm (e.g. $$L_ 1$$-estimates) are known. The methods are essentially functional analytical.

##### MSC:
 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35K35 Initial-boundary value problems for higher-order parabolic equations 47J05 Equations involving nonlinear operators (general)
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