Related papers: Global existence for reaction-diffusion evolution …
We consider reaction-diffusion equations either posed on Riemannian manifolds or in the Euclidean weighted setting, with pow\-er-type nonlinearity and slow diffusion of porous medium time. We consider the particularly delicate case $p<m$ in…
We consider the porous medium equation with a power-like reaction term, posed on Riemannian manifolds. Under certain assumptions on $p$ and $m$ in (1.1), and for small enough nonnegative initial data, we prove existence of global in time…
It is well known from the work of [2] that the Fujita phenomenon for reaction-diffusion evolution equations with power nonlinearities does not occur on the hyperbolic space $\mathbb{H}^N$, thus marking a striking difference with the…
We show a global existence result for a doubly nonlinear porous medium type equation of the form $$u_t = \Delta_p u^m +\, u^q$$ on a complete and non-compact Riemannian manifold $M$ of infinite volume. Here, for $1<p<N$, we assume…
This paper establishes the emergence of slowly moving transition layer solutions for the $p$-Laplacian (nonlinear) evolution equation, \[ u_t = \varepsilon^p(|u_x|^{p-2}u_x)_x - F'(u), \qquad x \in (a,b), \; t > 0, \] where $\varepsilon>0$…
We establish the global existence of higher-order Sobolev solutions for a non-local integrable evolution equation arising in the study of pseudospherical surfaces and non-linear wave propagation. Under a natural assumption on the initial…
We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including the Porous Medium Equation and the p-Laplacian with a…
We present a full classification of the short-time behaviour of the interfaces and local solutions to the nonlinear parabolic $p$-Laplacian type reaction-diffusion equation of non-Newtonian elastic filtration \[…
In this work we prove global existence and uniform boundedness of solutions of 2X2 reaction-diffusion systems with control of mass structure and nonlinearities of unlimited growth. Furthermore the results are obtained without restrictions…
In this paper, we consider a non-local diffusion equation involving the fractional $p(x)$-Laplacian with nonlinearities of variable exponent type. Employing the sub-differential approach we establish the existence of local solutions. By…
The goal of this work is to establish the global existence of nonnegative classical solutions in all dimensions for a system of highly nonlinear reaction-diffusion equations. We address the case for different diffusion coefficients and the…
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…
We prove the existence of global-in-time regular solutions to a system of stochastic quadratic reaction-diffusion equations. Global-in-time existence is based on a $L^\infty$-estimate obtained by an approach {\`a} la De Giorgi, as in…
The global existence of classical solutions to reaction-diffusion systems in dimensions one and two is proved. The considered systems are assumed to satisfy an {\it entropy inequality} and have nonlinearities with at most cubic growth in 1D…
In this paper, we prove the global existence of solutions to the relativistic Vlasov-Poisson system for general initial data in convex bounded domains of two space dimensions, assuming the specular reflection boundary conditions for the…
Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary…
This paper considers the existence of local and global-in-time strong solutions to the advection-diffusion equation with variable coefficients on an evolving surface with a boundary. We apply both the maximal $L^p$-in-time regularity for…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the…
We consider a model of fractional diffusion involving the natural nonlocal version of the $p$-Laplacian operator. We study the Dirichlet problem posed in a bounded domain $\Omega$ of ${\mathbb{R}}^N$ with zero data outside of $\Omega$, for…