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On the Boundary Value Condition of an Isotropic Parabolic Equation
Journal of Function Spaces ( IF 1.9 ) Pub Date : 2020-11-27 , DOI: 10.1155/2020/2180830 Qitong Ou 1 , Huashui Zhan 1
Journal of Function Spaces ( IF 1.9 ) Pub Date : 2020-11-27 , DOI: 10.1155/2020/2180830 Qitong Ou 1 , Huashui Zhan 1
Affiliation
The well-posedness problem of anisotropic parabolic equation with variable exponents is studied in this paper. The weak solutions and the strong solutions are introduced, respectively. By a generalized Gronwall inequality, the stability of strong solutions to this equation is established, and the uniqueness of weak solutions is proved. Compared with the related works, a new boundary value condition, , is introduced the first time and has been proved that it can take place of the Dirichlet boundary value condition in some way.
中文翻译:
各向同性抛物线方程的边值条件
研究了具有指数变化的各向异性抛物方程的适定性问题。分别介绍了弱解和强解。通过广义的Gronwall不等式,建立了该方程强解的稳定性,并证明了弱解的唯一性。与相关作品相比,一个新的边值条件,,介绍了第一次已经被证明,它可以发生在Dirichlet边界值条件的以某种方式。
更新日期:2020-11-27
中文翻译:
各向同性抛物线方程的边值条件
研究了具有指数变化的各向异性抛物方程的适定性问题。分别介绍了弱解和强解。通过广义的Gronwall不等式,建立了该方程强解的稳定性,并证明了弱解的唯一性。与相关作品相比,一个新的边值条件,,介绍了第一次已经被证明,它可以发生在Dirichlet边界值条件的以某种方式。