scholarly journals Convergence to steady states for a one-dimensional viscous Hamilton–Jacobi equation with Dirichlet boundary conditions

2007 ◽  
Vol 230 (2) ◽  
pp. 347-364 ◽  
Author(s):  
Philippe Laurençot
Keyword(s):  
Boundary Conditions ◽  
Jacobi Equation ◽  
Dirichlet Boundary ◽  
Steady States ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Convergence To Steady States ◽  
Hamilton Jacobi Equation

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals Convergence to steady states for radially symmetric solutions to a quasilinear degenerate diffusive Hamilton–Jacobi equation

2010 ◽  
Vol 67 (3-4) ◽  
pp. 229-250 ◽  
Author(s):  
Guy Barles ◽  
Philippe Laurençot ◽  
Christian Stinner
Keyword(s):  
Jacobi Equation ◽  
Steady States ◽  
Convergence To Steady States ◽  
Radially Symmetric Solutions ◽  
Hamilton Jacobi Equation

scholarly journals Reaction-advection-diffusion competition models under lethal boundary conditions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kwangjoong Kim ◽  
Wonhyung Choi ◽  
Inkyung Ahn
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Eigenvalue Problems ◽  
Reaction Diffusion ◽  
Steady States ◽  
Dirichlet Boundary Conditions ◽  
Hostile Environment ◽  
Directed Movement ◽  
Constant Rate ◽  
Homogeneous Dirichlet Boundary Conditions

<p style='text-indent:20px;'>In this study, we consider a Lotka–Volterra reaction–diffusion–advection model for two competing species under homogeneous Dirichlet boundary conditions, describing a hostile environment at the boundary. In particular, we deal with the case in which one species diffuses at a constant rate, whereas the other species has a constant rate diffusion rate with a directed movement toward a better habitat in a heterogeneous environment with a lethal boundary. By analyzing linearized eigenvalue problems from the system, we conclude that the species dispersion in the advection direction is not always beneficial, and survival may be determined by the convexity of the environment. Further, we obtain the coexistence of steady-states to the system under the instability conditions of two semi-trivial solutions and the uniqueness of the coexistence steady states, implying the global asymptotic stability of the positive steady-state.</p>

scholarly journals Triple solutions for a Dirichlet boundary value problem involving a perturbed discrete p(k)-Laplacian operator

2017 ◽  
Vol 15 (1) ◽  
pp. 1075-1089 ◽  
Author(s):  
Mohsen Khaleghi Moghadam ◽  
Johnny Henderson
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Local Minimum ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Laplacian Operator ◽  
Discrete Problem ◽  
Dirichlet Boundary Value Problem ◽  
One Dimensional ◽  
Minimum Theorem

Abstract Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k)-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.

Mild singular potentials as effective Laplacians in narrow strips

2017 ◽  
Vol 120 (1) ◽  
pp. 145
Author(s):  
César R. De Oliveira ◽  
Alessandra A. Verri
Keyword(s):  
Boundary Conditions ◽  
Quadratic Forms ◽  
Dirichlet Boundary ◽  
Schrödinger Operators ◽  
Dirichlet Boundary Conditions ◽  
Schrodinger Operators ◽  
Singular Potentials ◽  
One Dimensional ◽  
Effective Operators

We propose to obtain information on one-dimensional Schrödinger operators on bounded intervals by approaching them as effective operators of the Laplacian in thin planar strips.  Here we develop this idea to get spectral knowledge of some mild singular potentials with Dirichlet boundary conditions.  Special preparations, including a result on perturbations of quadratic forms, are included as well.

scholarly journals Further results for a one-dimensional linear thermoelastic equation with Dirichlet-Dirichlet boundary conditions

2002 ◽  
Vol 43 (3) ◽  
pp. 449-462 ◽  
Author(s):  
Bao Zhu Guo
Keyword(s):  
Hilbert Space ◽  
Boundary Conditions ◽  
Riesz Basis ◽  
Dirichlet Boundary ◽  
The State ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Parallel Result ◽  
Generalized Eigenfunctions ◽  
Thermoelastic Equation

AbstractWe show that a sequence of generalized eigenfunctions of a one-dimensional linear thermoelastic system with Dirichiet-Dirichlet boundary conditions forms a Riesz basis for the state Hilbert space. This develops a parallel result for the same system with Dirichlet-Neumann or Neumann-Dirichlet boundary conditions.

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