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44,760
SINGULAR NONLINEAR DIFFUSION EQUATIONS
"... (1) u t = (k(u,X)Ux) x (2) u t = k(ux)Uxx have been studied recently by many authors. The coefficient k is assumed to be positive on positive arguments and may represent the influences of thermal ..."
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(1) u t = (k(u,X)Ux) x (2) u t = k(ux)Uxx have been studied recently by many authors. The coefficient k is assumed to be positive on positive arguments and may represent the influences of thermal
Discrete Approximation of Nonlinear Diffusion Equation ♮
"... The paper deals with the approximation of some nonlinear diffusion equations with source terms and nonhomogeneous Dirichlet boundary conditions and initial conditions. The approximation scheme consists in the discretization of space derivative operators while the time differentiation is kept contino ..."
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The paper deals with the approximation of some nonlinear diffusion equations with source terms and nonhomogeneous Dirichlet boundary conditions and initial conditions. The approximation scheme consists in the discretization of space derivative operators while the time differentiation is kept
Finite Volumes and Nonlinear Diffusion Equations.
, 1998
"... . In this paper we prove the convergence of a finite volume scheme to the solution of a Stefan problem, namely the nonlinear diffusion equation u t \Gamma \Delta'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori estimate ..."
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Cited by 5 (0 self)
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. In this paper we prove the convergence of a finite volume scheme to the solution of a Stefan problem, namely the nonlinear diffusion equation u t \Gamma \Delta'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori
Differential constraints and exact solutions of nonlinear diffusion equations
, 2002
"... The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries. ..."
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Cited by 7 (1 self)
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The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining equations used in the search for classical Lie symmetries.
PAINLEVE ANALYSIS OF A CLASS OF NONLINEAR DIFFUSION EQUATIONS
, 1995
"... We study the Painleve analysis for a class of nonlinear diffusion equations. We find that in some cases it has only the conditional Painleve property and in other cases, just the Painleve property. We also obtained special solutions. ..."
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Cited by 1 (0 self)
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We study the Painleve analysis for a class of nonlinear diffusion equations. We find that in some cases it has only the conditional Painleve property and in other cases, just the Painleve property. We also obtained special solutions.
Semidiscretization and longtime asymptotics of nonlinear diffusion equations
 IN PROCEEDINGS OF GRIP 2004 CONFERENCE IN RENNES, SPECIAL NUMBER OF COMM. MATH. SCI
, 2004
"... We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by n ..."
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Cited by 4 (3 self)
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by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the longtime asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact
A Wavelet Regularization for Nonlinear Diffusion Equations
, 2004
"... We are concerned with a wavelet–based treatment of nonlinear diffusion equations in the context of image processing. In particular, we focus on the Perona– Malik model as a suitable instrument for smoothing images while preserving edges. We are not exploring a complete new method of solving the Pero ..."
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Cited by 9 (0 self)
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We are concerned with a wavelet–based treatment of nonlinear diffusion equations in the context of image processing. In particular, we focus on the Perona– Malik model as a suitable instrument for smoothing images while preserving edges. We are not exploring a complete new method of solving
The approach of solutions of nonlinear diffusion equations to travelling wave solutions
, 1975
"... The paper is concerned with the asymptotic behavior as t, oo of solutions u(x, t) of the equation in the case utuxxf(u)=O, xe( ~, oo), f(0) =f(1) =0, f'(0)<0, f'(1)<0. Commonly, a travelling front solution u=U(xct), U(oo)=0, U(oo)=l, exists. The following types of global stab ..."
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Cited by 236 (5 self)
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The paper is concerned with the asymptotic behavior as t, oo of solutions u(x, t) of the equation in the case utuxxf(u)=O, xe( ~, oo), f(0) =f(1) =0, f'(0)<0, f'(1)<0. Commonly, a travelling front solution u=U(xct), U(oo)=0, U(oo)=l, exists. The following types of global
Results 1  10
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44,760