On the critical behavior for the semilinear biharmonic heat equation with forcing term in exterior domain
Tobakhanov N.N. Torebek B.T.
15 January 2026Academic Press Inc.
Journal of Differential Equations
2026#451
In this paper, we investigate the critical behavior of solutions to the semilinear biharmonic heat equation with forcing term f(x), under six homogeneous boundary conditions. This paper is the first since the seminal work by Bandle et al. (2000) [24], to focus on the study of critical exponents in exterior problems for semilinear parabolic equations with a forcing term. By employing a method of test functions and comparison principle, we derive the critical exponents pCrit in the sense of Fujita. Moreover, we show that pCrit=∞ if N=2,3,4 and [Formula presented] if N⩾5. The impact of the forcing term on the critical behavior of the problem is also of interest, and thus a second critical exponent in the sense of Lee-Ni, depending on the forcing term is introduced. We also discuss the case f≡0, and present the finite-time blow-up results and lifespan estimates of solutions for the subcritical and critical cases. The lifespan estimates of solutions are obtained by employing the method proposed by Ikeda and Sobajama (2019) [13].
Critical exponent , Existence , Exterior problem , Nonexistence
Text of the article Перейти на текст статьи
Department of Mathematics, Nazarbayev University, Astana, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Shevchenko street 28, Almaty, 050010, Kazakhstan
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026