Abstract
In this paper, a semilinear viscoelastic parabolic equation with nonlinear boundary flux is studied. Due to the comparison principle being invalid, potential well method and concavity argument are used to prove that the solutions blow up in finite time with positive initial energy. This result improves the one obtained by Han et al. (C. R. Math. Acad. Sci. Paris, Sér. I 353:825-830, 2015).
Highlights
1 Introduction In this paper, we are concerned with the blow-up properties of solutions to the semilinear initial boundary value problem of the following form:
During the past few years, much work has been done on the study of equations with memory terms, and remarkable progress has been made on the local and global existence, uniqueness, finite time blow-up and regularities of weak or classical solutions
We confine ourselves to the finite time blow-up property of solutions to Problem ( ), an important property possessed by many nonlinear evolution equations
Summary
1 Introduction In this paper, we are concerned with the blow-up properties of solutions to the semilinear initial boundary value problem of the following form: During the past few years, much work has been done on the study of equations with memory terms, and remarkable progress has been made on the local and global existence, uniqueness, finite time blow-up and regularities of weak or classical solutions. We confine ourselves to the finite time blow-up property of solutions to Problem ( ), an important property possessed by many nonlinear evolution equations.
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