Nonexistence results for a higher-order evolution equation with an inhomogeneous term depending on time and space

2019/10/04 by Mohamed Jleli, Jleli, Mohamed, N. Lai +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.01790

openalex publication_date 2019/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a higher-order evolution equation with an inhomogeneous term depending on time and space. We first derive a general criterion for the nonexistence of weak solutions. Next, we study the particular case when the inhomogeneity depends only on space. In that case, we obtain the first critical exponent in the sense of Fujita, as well as the second critical exponent in the sense of Lee and Ni.

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