Results 131 to 140 of about 49,802 (165)
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2004
We shall consider here a stochastic heat equation pertubed by a polynomial term off odd degree d > 1 having negative leading coefficient (this will ensure non-explosion). We can represent this polynomial as \(\begin{array}{*{20}{c}} {\lambda \xi - p(\xi ),} & {\xi \in \mathbb{R},} \\ \end{array}\) where λ ∈ ℝ and p is an increasing polynomial, that is ...
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We shall consider here a stochastic heat equation pertubed by a polynomial term off odd degree d > 1 having negative leading coefficient (this will ensure non-explosion). We can represent this polynomial as \(\begin{array}{*{20}{c}} {\lambda \xi - p(\xi ),} & {\xi \in \mathbb{R},} \\ \end{array}\) where λ ∈ ℝ and p is an increasing polynomial, that is ...
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Travelling Waves for Reaction Diffusion Equations
Journal of Partial Differential Equations, 1997The paper deals with the travelling wave solution \(u(x,t)=u(x+kt)\) \((k>0)\) of the reaction diffusion equation: \[ u_t=u_{xx}+f(x),\quad u(+\infty)=H\quad\text{and }u(-\infty)=0\quad\text{for some }H>0, \] where the nonlinear term \(f(u)\) is assumed to be Lipschitz continuous and to satisfy \(f(0)=f(H)=0\) and \(\int^H_0f(s)ds>0\).
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Periodic Solutions to Reaction-Diffusion Equations
SIAM Journal on Applied Mathematics, 1976In this note we derive asymptotic formulas for rotating-spiral and axisymmetric, time-periodic solutions to reaction-diffusion systems.
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On the Existence of Pulses in Reaction- Diffusion- Equations
Results in Mathematics, 1992The author applies the theory of invariant manifolds for singularly perturbed ordinary differential equations and results about the persistence of homoclinic orbits in autonomous differential systems with several parameters in order to establish the existence of pulses in reaction-diffusion systems. Essential assumptions for the existence of pulses are
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Reaction - diffusion equations in perforated media
Nonlinearity, 1997The author considers the problem \[ {\partial\over\partial t} u(t,x)= {1\over 2} \sum^r_{i,j= 1} a_{ij}(x){\partial^2\over \partial x_i\partial x_j} u(t,x)+ \sum^r_{i= 1} b_i(x){\partial\over\partial x_i} u(t,x),\;t\in (0,\infty),\;x\in D= \mathbb{R}^r\setminus \bigcup^\infty_{i= 1} H_i, \] \[ {\partial u\over\partial n}+ f(x,u)= 0,\;x\in\bigcup ...
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Global solutions of reaction-diffusion equations
Funkcialaj Ekvacioj, 1987An a priori estimate of solutions of the Dirichlet problem for the quasilinear parabolic equation \[ (1)\quad u_ t=\sum_{i,j}(a_{ij}(t,x,u,\nabla u))_{x_ i}+\sum_{i}b_ i(t,x,u,\nabla u)u_{x_ i}+f(t,x,u,\nabla u) \] (t\(\geq 0,x\in \Omega \subset R^ n\), \(\Omega\) bounded smooth) in the \(L^{\infty}\) norm is presented first.
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On the Solution of Reaction—Diffusion Equations
IMA Journal of Applied Mathematics, 1981openaire +1 more source
Shadow systems and attractors in reaction-diffusion equations
Applicable Analysis, 1989Jack K Hale
exaly