Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWell-posedness of the fully coupled quasi-static thermo-poro-elastic equations with nonlinear convective transport
116
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biots model). It consists of a momentum balance equation, a mass balance equation, and an energy balance equation, fully coupled and nonlinear due to a convective transport term in the energy balance equation. The aim of this article is to investigate, in the context of mixed formulations, the existence and uniqueness of a weak solution to this model problem. The primary variables in these formulations are the fluid pressure, temperature and elastic displacement as well as the Darcy flux, heat flux and total stress. The well-posedness of a linearized formulation is addressed first through the use of a Galerkin method and suitable a priori estimates. This is used next to study the well-posedness of an iterative solution procedure for the full nonlinear problem. A convergence proof for this algorithm is then inferred by a contraction of successive difference functions of the iterates using suitable norms.
rate research
Read More
In this paper, we investigate the one-dimensional derivative nonlinear Schrodinger equations of the form $iu_t-u_{xx}+ilambdaabs{u}^k u_x=0$ with non-zero $lambdain Real$ and any real number $kgs 5$. We establish the local well-posedness of the Cauchy problem with any initial data in $H^{1/2}$ by using the gauge transformation and the Littlewood-Paley decomposition.
In this paper, we discuss the well-posedness of the Cauchy problem associated with the third-order evolution equation in time $$ u_{ttt} +A u + eta A^{frac13} u_{tt} +eta A^{frac23} u_t=f(u) $$ where $eta>0$, $X$ is a separable Hilbert space, $A:D(A)subset Xto X$ is an unbounded sectorial operator with compact resolvent, and for some $lambda_0>0$ we have $mbox{Re}sigma(A)>lambda_0$ and $f:D(A^{frac13})subset Xto X$ is a nonlinear function with suitable conditions of growth and regularity.
The aim of this paper is to establish the $H^1$ global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the asymptotic integrations for strictly hyperbolic systems with time-dependent coefficients. These integrations play an important role to setting the subsequent fixed point argument. The existence of solutions for less regular data is discussed, and several examples and applications are presented.
This paper concerns the local well-posedness for the good Boussinesq equation subject to quasi-periodic initial conditions. By constructing a delicately and subtly iterative process together with an explicit combinatorial analysis, we show that there exists a unique solution for such a model in a small region of time. The size of this region depends on both the given data and the frequency vector involved. Moreover the local solution has an expansion with exponentially decaying Fourier coefficients.
In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $partial_{t} u+ Delta^2 u=f(u),;t>0,;xinR^N,$ with $f(u)sim mbox{e}^{u^2}$ for large $u.$ Under smallness condition on the initial data and for exponential nonlinearity $f$ such that $f(u)sim u^m$ as $uto 0,$ $m$ integer and $N(m-1)/4geq 2$, we show that the solution is global. Moreover, we obtain a decay estimates for large time for the nonlinear biharmonic heat equation as well as for the nonlinear heat equation. Our results extend to the nonlinear polyharmonic heat equation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
