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Some problems on super-diffusions and one class of nonlinear differential equations

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Abstract

The historical superprocesses are considered on bounded regular domains with a complete branching form, as a probabilistic argument, the limit property of superprocesses is studied when the domains enlarge to the whole space. As an important application of superprocess, the representation of solutions of involved differential equations is used in term of historical superprocesses. The differential equations including the existence of nonnegative solution, the closeness of solutions and probabilistic representations to the maximal and minimal solutions are discussed, which helps develop the well-known results on nonlinear differential equations.

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Authors and Affiliations

  1. Department of Mathematics, Nankai University, 300071, Tianjin, Tianjin, China

    Wang Yongjin

  2. Centre for Advanced Study, Tsinghua University, 100084, Beijing, China

    Ren Yanxia

Authors
  1. Wang Yongjin
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  2. Ren Yanxia
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Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 19631060) and the Postdoctoral Foundation of China.

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Wang, Y., Ren, Y. Some problems on super-diffusions and one class of nonlinear differential equations. Sci. China Ser. A-Math. 42, 347–356 (1999). https://doi.org/10.1007/BF02874253

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  • DOI: https://doi.org/10.1007/BF02874253

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