Abstract In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and asymptotic behavior of the global solution and the blowup phenomena of solution with subcritical initial energy are established. Then these results are extended parallelly to the critical initial energy. Further the blowup phenomena of solution with supercritical initial energy is proved, but the existence, uniqueness and asymptotic behavior of the global solution with supercritical initial energy are still open.

中文翻译：

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非局部半线性伪抛物线方程的全局存在性和有限时间膨胀

摘要 在本文中，研究了非局部半线性拟抛物线方程的初边值问题，该问题被引入到种群动力学和生物科学中化学或生物体总质量守恒的建模现象中。建立了全局解的存在性、唯一性和渐近行为以及亚临界初能解的爆破现象。然后将这些结果平行扩展到临界初始能量。进一步证明了具有超临界初能的解的爆破现象，但具有超临界初能的全局解的存在性、唯一性和渐近行为仍然是开放的。