Levy driven stochastic heat equation with logarithmic nonlinearity: Well-posedness and Large deviation principle

2024/09/06 by R. Kavin, R, Kavin, Ananta K. Majee +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Mathematical Biology Tumor Growth #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2409.03991

Abstract

In this article, we study the well-posedness theory for solutions of the stochastic heat equations with logarithmic nonlinearity perturbed by multiplicative Levy noise. By using Aldous tightness criteria and Jakubowski version of the Skorokhod theorem on non-metric spaces along with the standard L2 method, we establish the existence of a path-wise unique strong solution. Moreover, by using a weak convergence method, we establish a large deviation principle for the strong solution of the underlying problem. Due to the lack of linear growth and locally Lipschitzness of the nonlinear term present in the underlying problem, the logarithmic Sobolev inequality and the nonlinear versions of Gronwall inequalities play a crucial role.

Cited by

• Global well-posedness for hyperbolic SPDEs with non-Lipschitz coefficients driven by space-time Lévy white noise
• L²-solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise^
• A stochastic heat equation with non-locally Lipschitz coefficients

Related

• Large deviations of stochastic heat equations with logarithmic nonlinearity
• Stochastic heat equations with logarithmic nonlinearity
• Large deviations for stochastic heat equations with memory driven by\n Levy-type noise
• Stochastic logarithmic Schrödinger equations driven by Lévy noise
• Large deviations for stochastic PDE with Levy noise