scholarly journals Problem with two-point conditions for parabolic equation of second order on time

2014 ◽  
Vol 6 (2) ◽  
pp. 351-359 ◽  
Author(s):  
M.M. Symotyuk ◽  
I.R. Tymkiv
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Second Order ◽  
Time Variable ◽  
Small Denominators ◽  
Dirichlet Type ◽  
Linear Parabolic Equations

The  correctness of the problem with two-point conditions on time variable and Dirichlet-type conditions  on spetial coordinates for the linear  parabolic equations are established. The metric theorem about estimate from below of small denominators of the problem is proved.

On the solutions of the first boundary value problem for the linear parabolic equations

1988 ◽  
Vol 108 (3-4) ◽  
pp. 339-355 ◽  
Author(s):  
Eugenio Sinestrari ◽  
Wolf von Wahl
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Second Order ◽  
Inhomogeneous Term ◽  
Hölder Continuous ◽  
Space And Time ◽  
Order Parabolic Equation ◽  
Linear Parabolic Equations

SynopsisThe first boundary value problem for a linear second order parabolic equation is studied under the assumption that the inhomogeneous term is continuous in space and time and Hölder-continuous only with respect to the space variables.

CAUCHY–DIRICHLET PROBLEM ASSOCIATED TO DIVERGENCE FORM PARABOLIC EQUATIONS

2004 ◽  
Vol 06 (03) ◽  
pp. 377-393 ◽  
Author(s):  
MARIA ALESSANDRA RAGUSA
Keyword(s):  
Parabolic Equation ◽  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Discontinuous Coefficients ◽  
Divergence Form ◽  
Second Order ◽  
Linear Parabolic Equation

In this note we study the Cauchy–Dirichlet problem related to a linear parabolic equation of second order in divergence form with discontinuous coefficients. Moreover we prove estimates in the space [Formula: see text], for every 1<p<∞.

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