相关论文: Towards the KPP--Problem and log t-Front Shift for…

It is shows that some aspects of classic KPP-problem (1937) can be extended to some fourth and sixth-order quasilinear parabolic equations.

Some extensions of the KPP idelogy of 1937 and more recent results to higher-order semilinear parabolic equations are discussed

Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of…

We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…

Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by elliptic equations with non-Lipschitz nonlinearities. Variational…

We use a new method in the study of Fisher-KPP reaction-diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of…

We study front propagation phenomena for a large class of nonlocal KPP-type reaction-diffusion equations in oscillatory environments, which model various forms of population growth with periodic dependence. The nonlocal diffusion is an…

The examples are considered of integrable hyperbolic equations of third order with two independent variables. In particular, an equation is found which admits as evolutionary symmetries the Krichever--Novikov equation and the modified…

This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…

For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.

We study propagation over $\mathbb{R}^d$ of the solution to a nonlocal nonlinear equation with anisotropic kernels, which can be interpretted as a doubly nonlocal reaction-diffusion equation of the Fisher--KPP-type. We prove that if the…

We analyze numerically a forward-backward diffusion equation with a cubic-like diffusion function, -emerging in the framework of phase transitions modeling- and its "entropy" formulation determined by considering it as the singular limit of…

This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87…

We prove the convergence of hyperbolic approximations for several classes of higher-order PDEs, including the Benjamin-Bona-Mahony, Korteweg-de Vries, Gardner, Kawahara, and Kuramoto-Sivashinsky equations, provided a smooth solution of the…

A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface…

Various shock and rarefaction-type similarity solutions of the third-order nonlinear dispersion equation in 1D are constructed. Blow-up of some solutions are proved by different techniques.

This paper is devoted to the analysis of the large-time behavior of solutions of one-dimensional Fisher-KPP reaction-diffusion equations. The initial conditions are assumed to be globally front-like and to decay at infinity towards the…

We extend the Riemann-Hilbert (RH) method to study the inverse scattering transformation and high-order pole solutions of the focusing and defocusing nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV) equations with nonzero…

We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…

In this paper we employ a "direct method" in order to obtain rank-k solutions of any hyperbolic system of first order quasilinear differential equations in many dimensions. We discuss in detail the necessary and sufficient conditions for…