arXiv subjects

Cristina Marcelli

Publications and source records attributed to Cristina Marcelli.

6 recordsLinked to original sources

arXiv2025

Finite propagation and saturation in reaction-diffusion-advection equations governed by p-Laplacian operator

The paper concerns front propagation for the following mono-stable reaction-diffusion-advection equation \[f(u)u_x + g(u)u_τ= [d(u)|u_x|^{p-2} u_x]_x+ ρ(u), \quad (x,τ)\in \R\times [0,+\infty).\] Besides existence and non-existence results for traveling wave solutions, the main focus is their classification: we provide criteria to establish if they attain one or both the equilibria at a finite time and in this case, if they are continuable as $C^1$-solutions or if they are sharp solutions.

math.AP↗

arXiv2025

Solvability of Dirichlet boundary value problems governed by non-monotone differential operators

We prove existence results for Dirichlet boundary value problems for equations of the type \begin{align*} \left( Φ(k(t) x'(t) ) \right)' = f(t, x(t) , x'(t) ) \qquad \text{for a.e. } t \in I:=[0,T] , \end{align*} where $Φ: J \to \mathbb{R} $ is a generic possibly non-monotone differential operator defined in a open interval $J\subseteq \mathbb{R}$, $k:I \to \mathbb{R}$, $k$ is measurable with $k(t) >0$ for a.e. $t \in I$ and $f: \mathbb{R}^3 \to \mathbb{R}$ is a Carathéodory function. Under very mild assumptions, we prove the existence of solutions for suitably prescribed boundary conditions, and we also address the study of the existence of heteroclinic solutions on the half-line $[0,+\infty)$.

math.CA↗

arXiv2025

Traveling waves for highly degenerate and singular reaction-diffusion-advection equations with discontinuous coefficients

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are furnished. Under an additional hypothesis on the convection term, the set of admissible wave speeds is characterized in terms of the minimum wave speed, which is estimated through a double-sided bound.

math.AP↗

arXiv2025

Wavefront Solutions for Reaction-diffusion-convection Models with Accumulation Term and Aggregative Movements

In this paper we analyze the wavefront solutions of parabolic partial differential equations of the type \[ g(u)u_τ+f(u)u_{x}=\left(D(u)u_{x}\right)_{x}+ρ(u),\quad u\left(τ,x\right)\in[0,1] \] where the reaction term $ρ$ is of monostable-type. We allow the diffusivity $D$ and the accumulation term $g$ to have a finite number of changes of sign. We provide an existence result of travelling wave solutions (t.w.s.) together with an estimate of the threshold wave speed. Finally, we classify the t.w.s. between classical and sharp ones.

math.AP↗

arXiv2025

Solvability of a doubly singular boundary value problem arising in front propagation for reaction-diffusion equations

The paper deals with the solvability of the following doubly singular boundary value problem \[\begin{cases} \dot z = c g(u)-f(u) -\dfrac{h(u)}{z^α}\\ z(0^+)=0, z(1^-)=0, \ z(u)>0 \text{ in } (0,1)\end{cases}\] naturally arising in the study of the existence and properties of travelling waves for reaction-diffusion-convection equations governed by the $p-$Laplacian operator. Here $c,α$ are real parameters, with $α>0$, and $f,g,h$ are continuous functions in $[0,1]$, with \[ h(0)=h(1), \quad h(u)>0 \text{ in } (0,1).\]

math.AP↗

arXiv2020

Boundary value problems associated with singular strongly nonlinear equations with functional terms

We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type $$\big(Φ(k(t)\,x'(t))\big)' + f(t,\mathcal{G}_x(t))\,ρ(t, x'(t)) = 0$$ on a compact interval $[a,b]$. These equations are quite general due to the presence of a strictly increasing homeomorphism $Φ$, the so-called $Φ$-Laplacian operator, of a nonnegative function $k$, which may vanish on a set of null measure, and moreover of a functional term $\mathcal{G}_x$. We look for solutions, in a suitable weak sense, which belong to the Sobolev space $W^{1,1}([a,b])$. Under the assumptions of the existence of a well-ordered pair of upper and lower solutions and of a suitable Nagumo-type growth condition, we prove an existence result by means of fixed point arguments.

math.CA↗