一类带锥体退化粘弹性项的半线性伪抛物方程的解的存在性和膨胀性

IF 0.9 3区 数学 Q2 MATHEMATICS
Hang Liu, Shuying Tian
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引用次数: 0

摘要

在本文中,我们考虑了带有锥退化粘弹性项 $$begin{aligned} u_t+\Delta _{\mathbb B}^{2} u_t+\Delta _{\mathbb B}^{2}u-\int _0^t g(t-s)\Delta _{\mathbb B}^{2}u(s)ds=f(u),\\text{ in }\text{ int }\mathbb B}^{2}u-\int _0^t g(t-s)\Delta _{\mathbb B}^{2}u(s)ds=f(u),\\text{ in }\text{ int }\mathbb B}^{2}times (0,T) 的半线性伪抛物方程。\times (0,T), end{aligned}$$ with initial and boundary conditions, where \(f(u)=|u|^{p-2}u-\frac{1}{|\mathbb B|}\displaystyle \int _{mathbb B}|u|^{p-2}u\frac{dx_1}{x_1}dx'\).我们为初始数据构造了几个条件,这些条件会导致解的全局存在或解在有限时间内爆炸。此外,我们还给出了解的渐近行为和炸毁时间的边界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Existence and blow-up of solutions for a class of semilinear pseudo-parabolic equations with cone degenerate viscoelastic term

In this paper, we consider the semilinear pseudo-parabolic equation with cone degenerate viscoelastic term

$$\begin{aligned} u_t+\Delta _{\mathbb B}^{2} u_t+\Delta _{\mathbb B}^{2}u-\int _0^t g(t-s)\Delta _{\mathbb B}^{2}u(s)ds=f(u),\ \text{ in } \text{ int }\mathbb B\times (0,T), \end{aligned}$$

with initial and boundary conditions, where \(f(u)=|u|^{p-2}u-\frac{1}{|\mathbb B|}\displaystyle \int _{\mathbb B}|u|^{p-2}u\frac{dx_1}{x_1}dx'\). We construct several conditions for initial data which leads to global existence of the solutions or the solutions blowing up in finite time. Moreover, the asymptotic behavior and the bounds of blow-up time for the solutions are given.

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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
59
期刊介绍: The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
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