Fujita-type results for the semilinear heat equations driven by mixed local-nonlocal operators
Kumar V. Torebek B.T.
5 June 2026Academic Press Inc.
Journal of Differential Equations
2026#465
This paper explores the critical behavior of the semilinear heat equation ut+La,bu=|u|p+f(x), considering both the presence and absence of a forcing term f(x). The mixed local-nonlocal operator La,b=−aΔ+b(−Δ)s,a,b∈R+, incorporates both local and nonlocal Laplacians. We determine the Fujita-type critical exponents by considering the existence or nonexistence of global solutions. Interestingly, the critical exponent is determined by the nonlocal component of the operator and, as a result, coincides with that of the fractional Laplacian. In the case without a forcing term, our results improve upon recent findings by Biagi et al. (2025) [2] and Del Pezzo and Ferreira (2025) [6] . When a forcing term is included, our results refine those of Wang and Zhang (2020) [27] and complement the work of Majdoub (2023) [19] .
Blow-up , Critical exponents , Global existence , Heat equation , Mixed local-nonlocal operator
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, Ghent, B 9000, Belgium
Department of Mathematical Sciences, Indian Institute of Technology (BHU), Uttar Pradesh, Varanasi, 221005, India
Institute of Mathematics and Mathematical Modeling, 28 Shevchenko str., Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis
Department of Mathematical Sciences
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