Construction of solutions of a partial differential equation with constant coefficients using the form of formal series. II

1994 ◽  
Vol 34 (2) ◽  
pp. 114-121 ◽  
Author(s):  
G. Dosinas ◽  
Z. Navickas
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Formal Series ◽  
Partial Differential ◽  
Constant Coefficients

A Tartar approach to periodic homogenization of linear hyperbolic stochastic partial differential equation

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640020 ◽  
Author(s):  
Mogtaba Mohammed ◽  
Mamadou Sango
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Original Problem ◽  
Stochastic Partial Differential Equation ◽  
Periodic Homogenization ◽  
Test Functions ◽  
Partial Differential ◽  
Periodic Coefficients ◽  
Constant Coefficients

This paper deals with the homogenization of a linear hyperbolic stochastic partial differential equation (SPDE) with highly oscillating periodic coefficients. We use Tartar’s method of oscillating test functions and deep probabilistic compactness results due to Prokhorov and Skorokhod. We show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized linear hyperbolic SPDE with constant coefficients. We also prove the convergence of the associated energies.

The weighted reverse poincaré type inequality for the difference of two parabolic subsolutions

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Muhammad Shoaib Saleem ◽  
Kakha Shashiashvili ◽  
Malkhaz Shashiashvili
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Type Inequality ◽  
Uniform Norm ◽  
Parabolic Partial Differential Equation ◽  
Cylindrical Domain ◽  
Partial Differential ◽  
Constant Coefficients ◽  
New Type ◽  
The Difference

AbstractA new type weighted reverse Poincaré inequality is established for a difference of two continuous weak parabolic subsolutions of a linear second order uniformly parabolic partial differential equation with constant coefficients in the cylindrical domain.This inequality asserts that if two continuous weak parabolic subsolutions are close in the uniform norm, then their gradients are close in the weighted

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