From Newton's equation to fractional diffusion and wave equations.
Se exponen las estimaciones numéricas preliminares de las singularidades de una ecuación diferencial fraccionaria no lineal. Dicha ecuación aparece en el estudio de las ondas viajeras asociadas a una ecuación de ondas que es una interpolación entre la ecuación de ondas clásica y la ecuación de Benjamin-Ono.
We study the large-time behaviour of the nonlinear oscillator where and is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case with real, . We characterize the existence and behaviour of fast orbits, i.e., orbits that stop in finite time.
We establish the existence, uniqueness and main properties of the fundamental solutions for the fractional porous medium equation introduced in [51]. They are self-similar functions of the form with suitable and . As a main application of this construction, we prove that the asymptotic behaviour of general solutions is represented by such special solutions. Very singular solutions are also constructed. Among other interesting qualitative properties of the equation we prove an Aleksandrov reflection...
We review the main mathematical questions posed in blow-up problems for reaction-diffusion equations and discuss results of the author and collaborators on the subjects of continuation of solutions after blow-up, existence of transient blow-up solutions (so-called peaking solutions) and avalanche formation as a mechanism of complete blow-up.
We study the large-time behaviour of the nonlinear oscillator where and is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case with real, . We characterize the existence and behaviour of fast orbits, , orbits that stop in finite time.
We establish the uniqueness of fundamental solutions to the p-Laplacian equation ut = div (|Du|p-2 Du), p > 2, defined for x ∈ RN, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equation ut...
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