Abstract
The aim of this paper is to study the existence and uniqueness of weak solutions for an initial boundary problem of a fourth-order parabolic equation with variable exponent of nonlinearity. First, the authors of this paper apply Leray-Schauder’s fixed point theorem to prove the existence of solutions of the corresponding nonlinear elliptic problem and then obtain the existence of weak solutions of nonlinear parabolic problem by combining the results of the elliptic problem with Rothe’s method. In addition, the authors also discuss the regularity of weak solutions in the case of space dimension one.
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Supported by NSFC (10771085), by Basic Research Foundation of Jilin University and by the 985 program of Jilin University.
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Guo, B., Gao, W. Study of weak solutions for a fourth-order parabolic equation with variable exponent of nonlinearity. Z. Angew. Math. Phys. 62, 909–926 (2011). https://doi.org/10.1007/s00033-011-0148-x
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DOI: https://doi.org/10.1007/s00033-011-0148-x