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Flandoli, Franco.
Random Perturbation of PDEs and Fluid Dynamic Models École d’Été de Probabilités de Saint-Flour XL – 2010 / [electronic resource] : by Franco Flandoli. - IX, 176p. 10 illus. online resource. - Lecture Notes in Mathematics, 2015 0075-8434 ; .
1. Introduction to Uniqueness and Blow-up -- 2. Regularization by Additive Noise -- 3. Dyadic Models -- 4. Transport Equation -- 5. Other Models. Uniqueness and Singularities.
This volume deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.
9783642182310
Mathematics.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2
Random Perturbation of PDEs and Fluid Dynamic Models École d’Été de Probabilités de Saint-Flour XL – 2010 / [electronic resource] : by Franco Flandoli. - IX, 176p. 10 illus. online resource. - Lecture Notes in Mathematics, 2015 0075-8434 ; .
1. Introduction to Uniqueness and Blow-up -- 2. Regularization by Additive Noise -- 3. Dyadic Models -- 4. Transport Equation -- 5. Other Models. Uniqueness and Singularities.
This volume deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.
9783642182310
Mathematics.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2