Related papers: Remarks on graph-like forward self-similar solutio…
In this article, we study the long-time asymptotic properties of a non-linear and non-local equation of diffusive type which describes the rock-paper-scissors game in an interconnected population.We fully characterize the self-similar…
We prove the existence of a large class of global-in-time expanding solutions to vacuum free boundary compressible Euler flows without relying on the existence of an underlying finite-dimensional family of special affine solutions of the…
We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper bound on the Laplacian of the distance and a suitable…
In the broad range of studies related to quantum graphs, quantum graph spectra appear as a topic of special interest. They are important in the context of diffusion type problems posed on metric graphs. Theoretical findings suggest that…
We prove the existence of a (spectrally) stable self-similar blow-up solution $f_0$ to the heat flow for corotational harmonic maps from $\mathbb R^3$ to the three-sphere. In particular, our result verifies the spectral gap conjecture…
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…
We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion…
The paper is devoted to the investigation of a reaction-diffusion system of equations describing the process of blood coagulation. Existence of pulses solutions, that is, positive stationary solutions with zero limit at infinity is studied.…
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which allows for the modeling of the dynamics of interfaces between…
We study a system of equations arising in the Chern-Simons model on finite graphs. Using the iteration scheme and the upper and lower solutions method, we get existence of solutions in the non-critical case. The critical case is dealt with…
Let $n\ge 3$, $0<m<\frac{n-2}{n}$, $\gamma>0$ and $\eta>0$. Suppose either (i) $\alpha\ne 0$ and $\beta=0$ or (ii) $\alpha\in\mathbb{R}$ and $\beta\ne 0$ holds. We will study the elliptic equation $\Delta (f^m/m)+\alpha f+\beta x\cdot\nabla…
In recent years the topic of localized wave solutions of the homogeneous scalar wave equation, i.e., the wave fields that propagate without any appreciable spread or drop in intensity, has been discussed in many aspects in numerous…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
Previous works for a liquid suddenly contacting a gas at a supercritical pressure show the coexistence of both phases and the generation of diffusion layers on both sides of the liquid-gas interface due to thermodynamic phase equilibrium. A…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs)…
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…
In this paper, we consider a family of piecewise constant solutions of the quasi-geostrophic shallow-water (QGSW) equation. We derive the contour dynamics equation of the QGSW front, which is a nonlinear, nonlocal dispersive equation, and…