Large stable pulse solutions in reaction-diffusion equations
نویسندگان
چکیده
منابع مشابه
Large Stable Pulse Solutions in Reaction-diffusion Equations
In this paper we study the existence and stability of asymptotically large stationary multi-pulse solutions in a family of singularly perturbed reaction-diffusion equations. This family includes the generalized Gierer-Meinhardt equation. The existence of N-pulse homoclinic orbits (N ≥ 1) is established by the methods of geometric singular perturbation theory. A theory, called the NLEP (=NonLoca...
متن کاملNumerical solutions for fractional reaction-diffusion equations
Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...
متن کاملThe Whitham principle for multikink solutions of reaction-diffusion equations
An useful strategy for the study of nonlinear partial differential equations (PDE) arising in pattern formation is to consider asymptotic solutions containing one or several localized defects and to simplify the dynamics by finding the equations of motion of the system of interacting defects. The great advantage of this approach is that we are dealing with ordinary differential equations (ODEs)...
متن کاملOn Existence and Nonexistence Global Solutions of Reaction-Diffusion Equations
We consider the initial value problem for the reaction-diffusion equation ut = ∆u + f(u). In this paper we show the existence and nonexistence of the global solutions in time. Especially, we extend the condition of the nonlinear terms to more general. We have the results of the existence and the nonexistence for the equation with the nonlinear term f satisfying lim infs→0 f(s)/sp > 0 and lim su...
متن کاملSpeed of wave-front solutions to hyperbolic reaction-diffusion equations.
The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2001
ISSN: 0022-2518
DOI: 10.1512/iumj.2001.50.1873