An Introduction to Fronts in Random Media (Google eBook)
This book gives a user friendly tutorial to Fronts in Random Media, an interdisciplinary research topic, to senior undergraduates and graduate students the mathematical sciences and engineering. The topics concerns both deterministic and probabilistic techniques. The approach taken uses elementary methods to introduce ideas and motivate results where possible. It takes a step by step approach, with exercises, allowing the reader to build up tools to use in research.
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assumptions asymptotic bistable boundary conditions Burgers equation cell problem central limit theorem Chapter coefﬁcients coercivity convergence convex covariance decay deﬁned denotes deterministic diffusion distribution equal exists exponential Feynman-Kac formula ﬁeld ﬁnite ﬁrst ﬂame follows front proﬁle front solutions front speed Fronts in Random function G-equation Gaussian process Hamilton–Jacobi equation Hamiltonian HJ equation holds implies inequality initial data integral KPP front speed Lagrangian large-deviation Lax formula Legendre transform Lemma linear Lipschitz continuous lower bound Lyapunov exponent maximum principle mean zero method minimal speed Neumann boundary condition nonlinearity nonnegative periodic media perturbation principal eigenvalue probability proof quadratic random media random variables reaction–diffusion satisﬁes scalar scaling shear ﬂow stationary stochastic homogenization subadditive ergodic theorem surely tion traveling fronts traveling-front unbounded uniformly unique upper bound variational formula vector velocity viscous Wiener process