Related papers: Global Existence for Reaction-diffusion Equations …
The paper concerns front propagation for the following mono-stable reaction-diffusion-advection equation \[f(u)u_x + g(u)u_\tau = [d(u)|u_x|^{p-2} u_x]_x+ \rho(u), \quad (x,\tau)\in \R\times [0,+\infty).\] Besides existence and…
This paper aims to prove the global existence of solutions for coupled reaction diffusion equations with a balance Law and nonlinearities with a non constant sign. The case when one (or both) of the components of the solution is not a…
Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…
The purpose of this paper is to prove global existence of solutions for general systems of reaction diffusion equations with nonlinearities for which only two main proprieties hold: Quasi-Positivity and balance law but with two…
The purpose of this paper is to give a necessary and sufficient condition for the existence and non-existence of global solutions of the following semilinear parabolic equations \[ u_{t}=\Delta u+\psi(t)f(u),\,\,\mbox{ in }\Omega\times…
In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: $\delta_tu = J \times u - u + f (x, u) t \in R^+, x \in R^N$, where J is a probability density and f is a KPP nonlinearity…
This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion \begin{align*} u_t=&\nabla\cdot(D(u)\nabla u)-\chi\nabla\cdot(u\nabla v)-\xi\nabla\cdot(u\nabla w)+\mu…
We consider the initial value problem for the thermal-diffusive combustion systems of the form: $u_{1,t}= Delta_{x}u_1 - u_1 u_2^m$, $u_{2,t}= d Delta_{x} u_2 + u_1 u_2^m$, $x in R^{n}$, $n geq 1$, $m geq 1$, $d > 1$, with bounded uniformly…
In this paper, we investigate the initial boundary value problem of the following nonlinear extensible beam equation with nonlinear damping term $$u_{t t}+\Delta^2 u-M\left(\|\nabla u\|^2\right) \Delta u-\Delta u_t+\left|u_t\right|^{r-1}…
It is shown that semilinear parabolic evolution equations $u'=A+f(t,u)$ featuring H\"older continuous nonlinearities $ f=f(t,u)$ with at most linear growth possess global strong solutions for a general class of initial data. The abstract…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
Our aim is to study the limit of the solution of reaction-diffusion porous medium equation with linear drift $\displaystyle\partial_t u -\Delta u^m +\nabla \cdot (u \: V)=g(t,x,u) $, as $m\to\infty.$ We study the problem in bounded domain…
Consider reaction-diffusion equation $u_t=\Delta u + f(x,u)$ with $x\in\mathbb{R}^d$ and general inhomogeneous ignition reaction $f\ge 0$ vanishing at $u=0,1$. Typical solutions $0\le u\le 1$ transition from $0$ to $1$ as time progresses,…
We study the uniform boundedness of solutions to reaction-diffusion systems possessing a Lyapunov-like function and satisfying an {\it intermediate sum condition}. This significantly generalizes the mass dissipation condition in the…
The global existence for semilinear wave equations with space-dependent critical damping $\partial_t^2u-\Delta u+\frac{V_0}{|x|}\partial_t u=f(u)$ in an exterior domain is dealt with, where $f(u)=|u|^{p-1}u$ and $f(u)=|u|^p$ are in mind.…
The present paper considers the Cauchy-Dirichlet problem for the time-nonlocal reaction-diffusion equation $$\partial_t (k\ast(u-u_0))+\mathcal{L}_x [u]=f(u),\,\,\,\, x\in\Omega\subset\mathbb{R}^n, t>0,$$ where $k\in…
The global boundedness and asymptotic behavior are investigated for the solutions of a nonlocal time fractional p-Laplacian reaction-diffusion equation (NTFPLRDE) $$ \frac{\partial^{\alpha }u}{\partial t^{\alpha }}=\Delta_{p} u+\mu…
In this article, we investigate the initial and boundary blow-up problem for the $p$-Laplacian parabolic equation $u_t-\Delta_p u=-b(x,t)f(u)$ over a smooth bounded domain $\Omega$ of $\mathbb{R}^N$ with $N\ge2$, where $\Delta_pu={\rm…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
We consider reaction-diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using Lyapunov functional and duality arguments, we establish…