Quantum Zakharov Model in a Bounded Domain

We consider an initial boundary value problem for a quantum version of the Zakharov system arising in plasma physics. We prove the global well-posedness of this problem in some Sobolev type classes and study properties of solutions. This result confirms the conclusion recently made in physical literature concerning the absence of collapse in the quantum Langmuir waves. In the dissipative case the existence of a finite dimensional global attractor is established and regularity properties of this attractor are studied. For this we use the recently developed method of quasi-stability estimates. In the case when external loads are $C^\infty$ functions we show that every trajectory from the attractor is $C^\infty$ both in time and spatial variables. This can be interpret as the absence of sharp coherent structures in the limiting dynamics.Comment: 27 page

Existence of radial stationary solutions for a system in combustion theory

In this paper, we construct radially symmetric solutions of a nonlinear noncooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. We prove the existence of 2 solutions using degree theory

SHANK3 controls maturation of social reward circuits in the VTA.

Haploinsufficiency of SHANK3, encoding the synapse scaffolding protein SHANK3, leads to a highly penetrant form of autism spectrum disorder. How SHANK3 insufficiency affects specific neural circuits and how this is related to specific symptoms remains elusive. Here we used shRNA to model Shank3 insufficiency in the ventral tegmental area of mice. We identified dopamine (DA) and GABA cell-type-specific changes in excitatory synapse transmission that converge to reduce DA neuron activity and generate behavioral deficits, including impaired social preference. Administration of a positive allosteric modulator of the type 1 metabotropic glutamate receptors mGluR1 during the first postnatal week restored DA neuron excitatory synapse transmission and partially rescued the social preference defects, while optogenetic DA neuron stimulation was sufficient to enhance social preference. Collectively, these data reveal the contribution of impaired ventral tegmental area function to social behaviors and identify mGluR1 modulation during postnatal development as a potential treatment strategy