Non linear diffusion and wave damped propagation : weak solutions and statistical turbulence behavior
Luiz C L Botelho
TL;DR
This paper establishes mathematical proofs for the existence and uniqueness of weak solutions to certain nonlinear parabolic and hyperbolic equations influenced by structured turbulence modeled as colored noise.
Contribution
It provides new rigorous proofs for weak solutions in nonlinear PDEs with stochastic initial conditions involving colored noise.
Findings
Existence of weak solutions is proven.
Uniqueness of solutions is demonstrated.
Analysis of turbulence behavior in nonlinear PDEs.
Abstract
We present mathematical proofs on the existence and uniqueness of weak solutions for a special class of non linear parabolic and hyperbolic equations of mathematical physics subject to colored noise (structured turbulence) as random- initial conditions
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Arctic and Antarctic ice dynamics · Differential Equations and Numerical Methods