Related papers: Exact solutions of nonlinear delay reaction-diffus…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or…
We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion-reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
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…
To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas…
This work investigates how we can extend the invariant subspace method to two-dimensional time-fractional non-linear PDEs. More precisely, the systematic study has been provided for constructing the various dimensions of the invariant…
A complete description of $Q$-conditional symmetries of reaction-diffusion-convection equation with arbitrary power nonlinearities is finished. It is shown that the results obtained in the first and second parts of this work (see…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
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…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
We consider the non-monotone degenerate diffusion equation with time delay. Different from the linear diffusion equation, the degenerate equation allows for semi-compactly supported traveling waves. In particular, we discover…
Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
This paper systematically explains how to apply the invariant subspace method using variable transformation for finding the exact solutions of the (k+1)-dimensional nonlinear time-fractional PDEs in detail. More precisely, we have shown how…
It is well recognized that in auxiliary equation methods, the exact solutions of different types of auxiliary equations may produce new types of exact travelling wave solutions to nonlinear partial differential equations in hand. In this…
The paper is devoted to a reaction-diffusion equation with delay arising in modelling the immune response. We prove the existence of travelling waves in the bistable case using the Leray-Schauder method. In difference with the previous…
In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our…