A transmission problem across a fractal self-similar interface

We consider a transmission problem in which the interior domain has infinitely ramified structures. Transmission between the interior and exterior domains occurs only at the fractal component of the interface between the interior and exterior domains. We also consider the sequence of the transmission problems in which the interior domain is obtained by stopping the self-similar construction after a finite number of steps; the transmission condition is then posed on a prefractal approximation of the fractal interface. We prove the convergence in the sense of Mosco of the energy forms associated with these problems to the energy form of the limit problem. In particular, this implies the convergence of the solutions of the approximated problems to the solution of the problem with fractal interface. The proof relies in particular on an extension property. Emphasis is put on the geometry of the ramified domain. The convergence result is obtained when the fractal interface has no self-contact, and in a particular geometry with self-contacts, for which an extension result is proved

Germination response of common annual and perennial forbs to heat shock and smoke treatments in the Chaco Serrano, central Argentina

Fire is a key ecological factor affecting plant dynamics. In the last few decades, fire occurrence in the Chaco region has increased noticeably, challenging the adaptive capacity of plants to regenerate after a fire. Broad-leaved forb species have been much less studied than woody and graminoids, although they are an important component of fire dynamics. Here we analysed the germination response to heat shock of 70 and 110°C, smoke and their combination in 10 broad-leaved herbaceous species frequently occurring in the Chaco Serrano of Córdoba province, central Argentina, including five annual (Bidens subalternans, Conyza bonariensis, Schkuhria pinnata, Tagetes minuta and Zinnia peruviana) and five perennial species (Borreria eryngioides, Sida rhombifolia, Solidago chilensis, Taraxacum officinale and Verbena litoralis). We also compared the response of annual versus perennial species. Six species had highest germination when treated with heat and smoke combined, whereas two had lowest germination under this treatment, indicating synergistic and antagonistic interaction of these factors respectively. Most of the species tolerated heat shock (i.e. germination was similar to that in control treatment), whereas others had higher germination in response to heat shock, especially under the moderate 70°C treatment. Germination was higher than control (i.e. no heat and no smoke) after smoke treatment in four species. Perennial species showed higher average germination than annuals in both heat treatments and in the control. Annual species had higher average germination for all treatments involving smoke. The high variability observed at the species level, and the limited number of species studied calls for precaution in interpreting and extrapolating results. Nevertheless, our study shows a general positive response of both perennial and annual species to fire cues, suggesting an advantage of these species for colonizing post-fire environments, and being favoured under scenarios of increasingly frequent low-to-medium intensity fires.Fil: Arcamone, Julieta Rocío. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Departamento de Diversidad Biológica y Ecológica. Cátedra de Ecología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; ArgentinaFil: Jaureguiberry, Pedro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; Argentin

Approximation of space-time fractional equations

The aim of this paper is to provide approximation results for space-time non-local equations with general non-local (and fractional) operators in space and time. We consider a general Markov process time changed with general subordinators or inverses to general subordinators. Our analysis is based on Bernstein symbols and Dirichlet forms, where the symbols characterize the time changes, and the Dirichlet forms characterize the Markov processes

Fractional equations via convergence of forms

We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in time

Sharp trudinger type inequalities for measure-valued lagrangeans

The aim of the paper is to prove weighted John-Nirenberg and sharp Trudinger type inequalities for measure-valued (α, p)-Lagrangeans

A numerical study of a degenerate diffusion equation driven by a Heaviside function

We analyze a nonlinear degenerate parabolic problem whose diffusion coefficient is the Heaviside function of the distance of the solution itself from a given target function. We show that this model behaves as an evolutive variational inequality having the target as an obstacle: under suitable hypotheses, starting from an initial state above the target the solution evolves in time towards an asymptotic solution, eventually getting in contact with part of the target itself. We also study a finite difference approach to the solution of this problem, using the exact Heaviside function or a regular approximation of it, showing the results of some numerical tests