Existence and uniqueness of solution for the stochastic nonlinear diffusion equation of plasma

TL;DR

This paper establishes the existence and uniqueness of strong solutions for a stochastic nonlinear diffusion equation modeling plasma behavior, involving super-fast diffusion and logarithmic nonlinearities.

Contribution

It provides a rigorous mathematical proof of existence and uniqueness for solutions to a specific stochastic plasma diffusion equation, addressing challenges posed by the nonlinear logarithmic term.

Findings

Proved existence of strong solutions.

Established uniqueness of solutions.

Addressed mathematical challenges of logarithmic nonlinearities.

Abstract

In this paper we are concerned with the stochastic partial differential equations of super-fast diffusion processes describing behavior of plasma dX(t)-{\Delta}ln(X(t)+1)dt=\surd(Q)dW(t), in (0,T)\timesO, where O is a bounded open subset of R. We define a strong solution adequate to the properties of the natural logarithm and we prove the corresponding existence and uniqueness result.