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Global existence for quasilinear diffusion equations in isotropic nondivergence form. (English) Zbl 1223.35202
The authors consider a quasilinear parabolic equation. By using the maximal regularity of a nonautonomous linear parabolic equation in the energy space, they are able to apply Schaefer’s fixed point theorem and prove global existence of a solution. Their result can be applied in several contexts.

MSC:
35K59 Quasilinear parabolic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35K10 Second-order parabolic equations
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