The functional constraints method: Application to non-linear delay reaction-diffusion equations with varying transfer coefficientsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 4 января 2018 г.
Аннотация:We present a number of new simple separable, generalized separable, and functional separable solutions to one-dimensional non-linear delay reaction-diffusion equations with varying transfer coefficients of the form u(t) = [G(u)u(x)](x) + F(u, w), where u = u(x, t) and w = u(x, t-tau), with tau denoting the delay time. All of the equations considered contain one, two, or three arbitrary functions of a single argument. The generalized separable solutions are sought in the form u = Sigma(N)(n) = (1)phi(n),(chi)psi(n)(t) with phi(n)(x) and psi(n)(t) to be determined in the analysis using a new modification of the functional constraints method. Some of the results are extended to non-linear delay reaction-diffusion equations with time-varying delay tau = tau(t). We also present exact solutions to more complex, three-dimensional delay reaction-diffusion equations of the form u(t) = div[G(u)del u]+F(u, w). Most of the solutions obtained involve free parameters and so may be suitable for solving certain problems as well as testing approximate analytical and numerical methods for non-linear delay PDEs.