6 papers
On semilinear Grushin--Schrödinger equation in
Jônison Carvalho, Arlúcio Viana
We establish the existence of nontrivial nonnegative weak solutions to the following equation \begin{equation*} -Î_γu + V(z)u = Q(z)f(u), \quad z\in \mathbb{R}^N, \end{equation*}…
Nonexistence of global solutions to the Grushin heat equation with nonlocal and local nonlinearities
Ahmad Z. Fino, Arlúcio Viana
In this paper, we investigate the nonexistence of global solutions to the Grushin-type heat equation with nonlinear reaction terms, including cases involving memory effects: $$ \le…
Duality estimates for subdiffusion problems including time-fractional porous medium type equations
Arlúcio Viana, Patryk Wolejko, Rico Zacher
We prove duality estimates for time-fractional and more general subdiffusion problems. An important example is given by subdiffusive porous medium type equations. Our estimates can…
On the semilinear heat equation with the Grushin operator
Geronimo Oliveira, Arlúcio Viana
In this work, we study the heat equation with Grushin's operator. We present an expression for its heat kernel, prove its decay in spaces, and that it is an approximation of…
On the Heat equation involving a Grushin operator in Marcinkiewcz spaces
Alessia E. Kogoj, Maria E. Lima, Arlúcio Viana
In this work, we give sufficient conditions for the existence and uniqueness of the heat equation involving the operator $$ Î_{\mathcal{G}}=\dfrac{1}{2}\left(Î_{x}+|x|^2Î_{y}\ri…
Local and global solvability of the Grushin heat equation with mixed nonlinear memory and reaction terms
Ahmad Z. Fino, Arlucio Viana
In this work, we investigate the solvability of a heat equation involving the Grushin operator. The equation is perturbed by two nonlinear reaction terms, one of which includes a m…