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Mild Solutions for the Stochastic Generalized Burgers–Huxley Equation

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Abstract

In this work, we consider the stochastic generalized Burgers–Huxley equation perturbed by space–time white noise and discuss the global solvability results. We show the existence of a unique global mild solution to such equation using a fixed point method and stopping time arguments. The existence of a local mild solution (up to a stopping time) is proved via contraction mapping principle. Then, establishing a uniform bound for the solution, we show the existence and uniqueness of global mild solution to the stochastic generalized Burgers–Huxley equation. Finally, we discuss the inviscid limit of the stochastic Burgers–Huxley equation to the stochastic Burgers as well as Huxley equations.

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Notes

  1. One has to write \(Au=-u''\).

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Acknowledgements

M. T. Mohan would like to thank the Department of Science and Technology (DST), India, for Innovation in Science Pursuit for Inspired Research (INSPIRE) Faculty Award (IFA17-MA110). The author sincerely would like to thank the reviewer for his/her valuable comments and suggestions, which helped to improve the manuscript significantly (especially in the proof of Lemma 3.3).

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  1. Department of Mathematics, Indian Institute of Technology Roorkee-IIT Roorkee, Haridwar Highway, Roorkee, Uttarakhand, 247667, India

    Manil T. Mohan

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Mohan, M.T. Mild Solutions for the Stochastic Generalized Burgers–Huxley Equation. J Theor Probab 35, 1511–1536 (2022). https://doi.org/10.1007/s10959-021-01100-w

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