The stability of the anisotropic parabolic equation with the variable exponent
نویسنده
چکیده
with ai(x),pi(x) ∈ C1( ), pi(x) > 1,ai(x)≥ 0. Basing on the weighted variable exponent Sobolev space, a new kind of weak solutions of the equation is introduced. Whether the usual Dirichlet homogeneous boundary value condition can be imposed depends on whether ai(x) is degenerate on the boundary or not. If some of {ai(x)} are degenerate on the boundary, a partial boundary value condition is imposed. If every ai(x) is degenerate on the boundary, by the new definition of a weak solution, the stability of weak solutions can be proved without any boundary value condition.
منابع مشابه
The Density-Driven Nanofluid Convection in an Anisotropic Porous Medium Layer with Rotation and Variable Gravity Field: A Numerical Investigation
In this study, a numerical examination of the significance of rotation and changeable gravitational field on the start of nanofluid convective movement in an anisotropic porous medium layer is shown. A model that accounts for the impact of Brownian diffusion and thermophoresis is used for nanofluid, while Darcy’s law is taken for the porous medium. The porous layer is subjected to uniform rotat...
متن کاملFinite time blow up of solutions of the Kirchhoff-type equation with variable exponents
In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.
متن کاملThermal Stability of Thin Rectangular Plates with Variable Thickness Made of Functionally Graded Materials
In this research, thermal buckling of thin rectangular plate made of Functionally Graded Materials (FGMs) with linear varying thickness is considered. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The supporting condition of all edges of such a plate is simply supported. ...
متن کاملThe fibering map approach to a quasilinear degenerate p(x)-Laplacian equation
By considering a degenerate $p(x)-$Laplacian equation, a generalized compact embedding in weighted variable exponent Sobolev space is presented. Multiplicity of positive solutions are discussed by applying fibering map approach for the corresponding Nehari manifold.
متن کاملSaint-Venant torsion of non-homogeneous anisotropic bars
The BEM is applied to the solution of the torsion problem of non-homogeneous anisotropic non-circular prismatic bars. The problem is formulated in terms of the warping function. This formulation leads to a second order partial differential equation with variable coefficients, subjected to a generalized Neumann type boundary condition. The problem is solved using the Analog Equation Method (AEM)...
متن کامل