Results 121 to 130 of about 65,920 (166)

Stochastic Nonlinear Diffusion Equations with Singular Diffusivity

SIAM Journal on Mathematical Analysis, 2009
This paper is concerned with the stochastic diffusion equation \(dX(t)=\text{div}[\text{sgn}(\nabla(X(t)))]dt+\sqrt{Q}dW(t)\) in \((0,\infty) \times \mathcal{O}\), where \(\mathcal{O}\) is a bounded open subset of \(\mathbb{R}^d, d=1,2, W(t)\) is a cylindrical Wiener process on \(L^2(\mathcal{O})\), and \(\text{sgn}(\nabla X)=\nabla X/|\nabla X|_d\) if
Barbu, Viorel, Da Prato, Giuseppe, Röckner, Michael   +2 more
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Nonlinear diffusion layers

Designs, Codes and Cryptography, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yunwen Liu, Vincent Rijmen, Gregor Leander   +2 more
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Nonlinear Diffusion Processes

Siberian Mathematical Journal, 2003
The author studies the elliptic system of first-order strongly nonlinear differential equations of one complex variable \[ u_{\bar z} = \mu^1u_z + \mu^2\bar u_{\bar z} + f \equiv A(z,u,v),\quad v = u_{z} \] which is commonly used to describe diffusion and convective processes of heat and mass transfer in a fluid.
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Asymptotic properties of nonlinear diffusion, nonlinear drift‐diffusion, and nonlinear reaction‐diffusion equations

Annalen der Physik, 2004
AbstractWe review a Fokker‐Planck approach to nonlinear evolution equations such as nonlinear diffusion equations and nonlinear drift‐diffusion equations and extend this approach to nonlinear reaction‐diffusion equations. Using this Fokker‐Planck approach along with appropriately defined entropy and free energy measures, we show that transient ...
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Nonlinear Diffusion with Absorption

Potential Analysis, 1997
The author studies the problem \[ u- \text{div }a(\cdot, \text{grad }u)+ \partial j(\cdot, u)\ni f\quad\text{on }\Omega,\quad u|_{\partial\Omega}= 0,\leqno E(j,f) \] where \(j:\Omega\times \mathbb{R}\to[0,\infty)\) is convex l.s.c. in \(r\in\mathbb{R}\) with \(j(\cdot,0)= 0\) [the absorption term is \(\partial j\) as subgradient of \(j\)].
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The Asymptotics of Nonlinear Diffusion

Studies in Applied Mathematics, 1970
The asymptotic behavior of linear diffusion processes may be significantly altered by weak nonlinear effects. A method is developed for investigating such situations. Examples of both deterministic and statistical initial value problems are discussed in the one dimensional case.
Benney, D. J., Lange, C. G.
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Nonlinear Diffusion of Biological Systems

Russian Physics Journal, 2014
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Lasukov, V. V., Lasukova, T. V.
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A Nonlinear Pseudoparabolic Diffusion Equation

SIAM Journal on Mathematical Analysis, 1985
Diffusion in a fissured medium with absorption or partial saturation effects leads to the initial-boundary value problem \[ (P)\quad u'+\epsilon^{-1}(\alpha (u)-v)=f_ 1,\quad -div(k(u)\nabla v)+\epsilon^{-1}(v-\alpha (u))=f_ 2\quad in\quad Q, \] u(x,0)\(=u_ 0(x)\), \(v_{\partial G}=0\), where \(S=[0,T]\), G is a smooth bounded domain in \(R^ N\) and ...
Böhm, Michael, Showalter, R. E.
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Nonlinear diffusion with linearly varying diffusivity

Journal of Hydrology, 1984
Abstract An approximate analytical solution to the nonlinear diffusion equation is presented. The diffusivity is assumed to be linearly dependent on concentration. The one-dimensional problem is reduced to an ordinary differential equation through the Boltzmann transformation and a technique which is exploiting basic characteristics of the exact ...
Panagiotis K. Tolikas, Epaminondas Sidiropoulos   +1 more
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