Functional separable solutions of nonlinear convection–diffusion equations with variable coefficientsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 29 мая 2019 г.
Аннотация:The paper presents a number of new functional separable solutions to nonlinear convection--diffusion equations of the form
$$c(x)u_t=[a(x)u_x]_x+[b(x)+p(x)f(u)]u_x,$$
where $f(u)$ is an arbitrary function. It shows that any three of the four variable coefficients $a(x)$, $b(x)$, $c(x)$, $p(x)$ of such equations can be chosen arbitrarily, and the remaining coefficient can be expressed through the others. Examples of specific equations and their exact solutions are given. The results obtained are generalized to more-complex nonlinear PDEs with variable coefficients. Also some functional separable solutions to nonlinear convection--diffusion equations with delay
$$u_t=u_{xx}+a(x)f(u,w)u_x,\quad \ w=u(x,t-\tau),$$
where $\tau>0$ is the delay time and $f(u,w)$ is an arbitrary function of two arguments, are obtained.