Global existence for nonlinear bi-parabolic equation under globally Lipschitz condition
Abstract
The bi-parabolic equation plays a large role in the theory of heat transfer. Our main goal is to consider the existence of a nonlinear bi-parabolic equation with globally Lipschitz of the source term. With some suitable conditions of the input data, we prove the global unique existence of the mild solution. The main technique in the paper is to use Banach’s fixed point theorem in combination with the \(L^p-L^q\) estimates. This paper seems to generalize previous results for the bi-parabolic equation in this direction.References
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