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• W2089373698 abstract "This paper is devoted to system of semilinear heat equations with exponential-growth nonlinearity in two-dimensional space which is the analogue of the scalar model problem studied in [S. Ibrahim, R. Jrad, M. Majdoub and T. Saanouni, Local well posedness of a 2D semilinear heat equation, Bull. Belg. Math. Soc.21 (2014) 1–17]. First, we prove the local existence and unconditional uniqueness of solutions in the Sobolev space (H 1 × H 1 )(ℝ 2 ). The uniqueness part is nontrivial although it follows Brezis–Cazenave's proof [H. Brezis and T. Cazenave, A nonlinear heat equation with singular initial data, J. Anal. Math.68 (1996) 73–90] in the case of monomial nonlinearity in dimension d ≥ 3. Next, we show that in the defocusing case our solution is bounded, and therefore exists globally in time. Finally, for this system, we treat the question of blow-up in finite time under the negativity condition on the energy functional. The technique to be used is adapted from [Bull. Belg. Math. Soc. 21 (2014) 1–17]." @default.
• W2089373698 created "2016-06-24" @default.
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• W2089373698 date "2015-03-01" @default.
• W2089373698 modified "2023-09-26" @default.
• W2089373698 title "The Cauchy problem for a system of nonlinear heat equations in two space dimensions" @default.
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• W2089373698 doi "https://doi.org/10.1142/s1793557115500047" @default.
• W2089373698 hasPublicationYear "2015" @default.
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