On Recent Progress for the Stochastic Navier Stokes Equations [PDF]
, 2003 We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations.
Mattingly, Jonathan C.
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Phase-field approaches to structural topology optimization [PDF]
, 2010 The mean compliance minimization in structural topology optimization is solved with the help of a phase field approach. Two steepest descent approaches based on L2- and H-1 gradient flow dynamics are discussed. The resulting flows are given by Allen-Cahn
Blank, Luise +5 more
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Infinite-dimensional parabolic equations in Gauss-Sobolev spaces [PDF]
, 2007 The paper is concerned with a class of parabolic equations with a gradient-dependent nonlinear term in a Gauss-Sobolev space setting. Un-der a local Lipschitz continuity condition, it is shown in Theorem 4.2 that there exists a unique strong solution of ...
Chow, Pao-Liu
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BSDE, Path-dependent PDE and Nonlinear Feynman-Kac Formula [PDF]
, 2011 In this paper, we introduce a type of path-dependent quasilinear (parabolic) partial differential equations in which the (continuous) paths on an interval [0,t] becomes the basic variables in the place of classical variables (t,x). This new type of PDE
Peng, Shige, Wang, Falei
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Closure properties of solutions to heat inequalities [PDF]
, 2008 We prove that if $u_1,u_2 : (0,\infty) \times \R^d \to (0,\infty)$ are sufficiently well-behaved solutions to certain heat inequalities on $\R^d$ then the function $u: (0,\infty) \times \R^d \to (0,\infty)$ given by $u^{1/p}=u_1^{1/p_1} * u_2^{1/p_2 ...
C. Borell +18 more
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Random nonlinear evolution inclusions in reflexive Banach spaces [PDF]
, 1988 In this paper we present two existence results for a large class of random, nonlinear, multivalued evolution equations defined in a reflexive, separable Banach space and involving an m m -dissipative operator.
Avgerinos, E, Papageorgiou, N
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Large scale dynamics of the Persistent Turning Walker model of fish behavior [PDF]
, 2007 International audienceThis paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory.
A. Aw +48 more
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On solving the nonlinear Biswas-Milovic equation with dual-power law nonlinearity using the extended tanh-function method [PDF]
, 2015 In this article, we apply the extended tanh-function method to find the exact traveling wave solutions of the nonlinear Biswas-Milovic equation (BME), which describes the propagation of solitons through optical fibers for trans-continental and trans ...
E. Zayed, Elsayed M.
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Electrical-thermal analytical modeling of monopolar RF thermal ablation of biological tissues: determining the circumstances under which tissue temperature reaches a steady state [PDF]
, 2016 This is a pre-copy-editing, author-produced PDF of an article accepted for publication in MATHEMATICAL BIOSCIENCES doi:10.3934/mbe.2015003 AND ENGINEERING following peer review. The definitive publisher-authenticated version Mathematical Biosciences and
A. Erez +25 more
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On the Cauchy problem for a semilinear fractional elliptic equation [PDF]
, 2018 We study, for the first time in the literature on the subject, the Cauchy problem for a semilinear fractional elliptic equation. Under an a priori assumption on the solution, we propose the Fourier truncation method for stabilizing the ill-posed problem.
Lesnic, D, Triet, NA, Tuan, NH, Xuan, TD
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