| Abstract: |
| We consider the initial boundary value problem of some doubly nonlinear parabolic equation with $p$-Laplacian ($p>1$). For the case where the exponent $p$ is sufficiently large, Barbu (1979) proved the solvability of this problem without any assumptions on the maximal monotone growth in the time-derivative term via some abstract problem in the Hilbert space. Main purpose of this talk is to show the existence of solution for every small $p$, where it is difficult to reduce the problem to the Hilbert setting. |
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