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Global solution for fully nonlinear parabolic equations in one-dimensional space

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Abstract

We discuss the existence of global classical solution for the uniformly parabolic equation

$$\left\{ \begin{gathered} u_t = a(x,t,u,u_x ,u_{xx} ) + b(x,t,u,u_x ), (x,t) \in ( - 1,1) \times (0,T], \hfill \\ u( \pm 1,t) = 0, u(x,0) = \varphi (x), \hfill \\ \end{gathered} \right.$$

Wherea is strongly nonlinear with respect tou xx and ϕ is not necessarily small. We also deal with nonuniform case.

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou University, 310028, Hangzhou, China

    Chen Shaohua

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  1. Chen Shaohua
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Supported by the Open Office of Mathematica Institute, Academia Sinica.

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Shaohua, C. Global solution for fully nonlinear parabolic equations in one-dimensional space. Acta Mathematica Sinica 10, 325–335 (1994). https://doi.org/10.1007/BF02560723

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  • DOI: https://doi.org/10.1007/BF02560723

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