Entire Solutions in Bistable Reaction-diffusion Equations with Nonlocal Delayed Nonlinearity

نویسندگان

  • ZHI-CHENG WANG
  • SHIGUI RUAN
چکیده

This paper is concerned with entire solutions for bistable reactiondiffusion equations with nonlocal delay in one-dimensional spatial domain. Here the entire solutions are defined in the whole space and for all time t ∈ R. Assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument, we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x-axis and annihilating at a finite time. Furthermore, we show that such an entire solution is unique up to space-time translations and is Liapunov stable. A key idea is to characterize the asymptotic behavior of the solutions as t → −∞ in terms of appropriate subsolutions and supersolutions. In order to illustrate our main results, two models of reaction-diffusion equations with nonlocal delay arising from mathematical biology are considered.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Traveling Wave Solutions for Bistable Differential-Difference Equations with Periodic Diffusion

We consider traveling wave solutions to spatially discrete reaction-diffusion equations with nonlocal variable diffusion and bistable nonlinearities. To find the traveling wave solutions we introduce an ansatz in which the wave speed depends on the underlying lattice as well as on time. For the case of spatially periodic diffusion we obtain analytic solutions for the traveling wave problem usin...

متن کامل

Bistable travelling waves for nonlocal reaction diffusion equations

We are concerned with travelling wave solutions arising in a reaction diffusion equation with bistable and nonlocal nonlinearity, for which the comparison principle does not hold. Stability of the equilibrium u ≡ 1 is not assumed. We construct a travelling wave solution connecting 0 to an unknown steady state, which is “above and away” from the intermediate equilibrium. For focusing kernels we ...

متن کامل

Travelling Fronts in Asymmetric Nonlocal Reaction Diffusion Equations: the Bistable and Ignition Cases

This paper is devoted to the study of the travelling front solutions which appear in a nonlocal reaction-diffusion equations of the form ∂u ∂t = J ⋆ u− u+ f(u). When the nonlinearity f is of bistable or ignition type, and the dispersion kernel J is asymmetric, the existence of a travelling wave is proved. The uniqueness of the speed of the front is also established. The construction of the fron...

متن کامل

Entire Solutions in Lattice Delayed Differential Equations with Nonlocal Interaction: Bistable Cases

This paper is concerned with entire solutions of a class of bistable delayed lattice differential equations with nonlocal interaction. Here an entire solution is meant by a solution defined for all (n, t) ∈ Z × R. Assuming that the equation has an increasing traveling wave front with nonzero wave speed and using a comparison argument, we obtain a two-dimensional manifold of entire solutions. In...

متن کامل

Traveling Wave Solutions for Bistable Diierential-diierence Equations with Periodic Diiusion Draft Version

We consider traveling wave solutions to spatially discrete reaction-diiusion equations with nonlocal variable diiusion and bistable nonlinearities. For the case of spatially periodic diiusion we obtain analytic solutions for the traveling wave problem using a piecewise linear nonlinearity. The formula for the wave forms is implicitly deened in the general periodic case and we provide an explici...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008