带不同幂次型非线性项的半线性三阶发展方程整体解的存在性与爆破

Abstract

Abstract:

This paper studies the Cauchy problem of a class of semilinear third-order evolution equations with different power-type nonlinear terms. Its linearized model is derived from the classical thermoelastic plate equations considering Fourier's law. Firstly, by using the appropriate $L^r\!-\!L^q$ estimation away from the asymptote and combining with the Banach fixed point theorem, the existence of the global solution under small initial conditions is obtained. Secondly, for the nonlinear terms that satisfy specific conditions, the explosion of the solution is proved by the test function method. Finally, based on these research results, some critical indicators of the semilinear third-order model are obtained.

Key words: Global existence of solution, Semilinear third order evolution equation, Blow-up, Thermoelastic plate equations

CLC Number:

0175.2

Shi Jincheng, Liu Yan. Global Existence and Blow-Up for Semilinear Third Order Evolution Equation with Different Power Nonlinearities[J].Acta mathematica scientia,Series A, 2024, 44(6): 1550-1562.

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References 43

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Global Existence and Blow-Up for Semilinear Third Order Evolution Equation with Different Power Nonlinearities

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