Related papers: The Cauchy Problem for a One Dimensional Nonlinear…
We consider the Cauchy problem for a system of fully nonlinear parabolic equations. In this paper, we shall show the existence of global-in-time solutions to the problem. Our condition to ensure the global existence is specific to the fully…
A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and…
We show the short time existence and uniqueness of solutions to the Cauchy problem for fully nonlinear systems of arbitrary even order on closed manifolds which are strongly parabolic at the initial values. The proof uses a linearization…
Although there are many results on the global solvability and the precise description of the large time behaviors of solutions to the initial-boundary value problems of the one-dimensional viscous radiative and reactive gas in bounded…
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is…
In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. Our aim is to obtain the threshold, to classify the global existence of solution for small data or the finite time…
We consider an evolution equation inspired by a model in peridynamics, with a singular pairwise interaction force term, and we give global in time existence, uniqueness and stability results for the Cauchy problem.
We prove the well-posedness of the Cauchy problem on torus to an eletromagnetoelastic system. The physical model consists of three coupled partial differential equations, one of them is a hyperbolic equation describing the elastic medium…
We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite times. Furthermore, we derive an…
We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in $% \mathbb{R}_{+}\times \mathbb{R}^{N}$. Under appropriate conditions on the exponents and the orders of…
The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global…
We study the Cauchy problem for the nonlinear damped wave equation and establish the large data local well-posedness and small data global well-posedness with slowly decaying initial data. We also prove that the asymptotic profile of the…
In this paper, we study the solvability of a Cauchy- Dirichlet problem for nonlinear parabolic equation with non standard growths and nonlocal terms. We show the existence of weak solutions of the considered problem under more general…
We study the Cauchy problem for a system of two coupled nonlinear focusing Schroedinger equations arising in nonlinear optics. We discuss when the solutions are global in time or blow-up in finite time. Some results, in dependence of the…
The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or…
We investigate the Cauchy problem of three-dimensional compressible non-isothermal nematic liquid crystal flows in $\mathbb{R}^3$. We derive the global existence and uniqueness of strong solutions with both interior and far field vacuum…
In this work I study the well-posedness of the Cauchy problem associated with the coupled Schr\"odinger equations {with quadratic nonlinearities}, which appears modeling problems in nonlinear optics. I obtain the local well-posedness for…
The Cauchy problem for a nonlinear elastic wave equations with viscoelastic damping terms is considered on the 3 dimensional whole space. Decay and smoothing properties of the solutions are investigated when the initial data are…
Solutions of the Cauchy problem for the wave equation on a non-globally hyperbolic spacetime, which contains closed timelike curves (time machines) are considered. It is proved, that there exists a solution of the Cauchy problem, it is…
Nonlinear elastic models are widely used to describe the elastic response of crystalline solids, for example, the well-known Cauchy-Born model. While the Cauchy-Born model only depends on the strain, effects of higher order strain gradients…