Abstract
Letu be a weak solution of the initial boundary value problem for the semilinear parabolic system of order 2m:u′(t)+Au(t)+f(t,.,u,..., ▽m u)=0. Letf satisfy controllable growth conditions. Thenu is smooth.
This result is proved by a kind of continuity method, where the timet is the parameter of continuity.
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Grunau, HC., von Wahl, W. Regularity of weak solutions of semilinear parabolic systems of arbitrary order. J. Anal. Math. 62, 307–322 (1994). https://doi.org/10.1007/BF02835960
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DOI: https://doi.org/10.1007/BF02835960