A dynamic boundary-value problem without initial conditions for almost linear parabolic equations

2010 ◽  
Vol 171 (4) ◽  
pp. 474-489
Author(s):  
Yu. B. Dmytryshyn
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Initial Conditions ◽  
Boundary Value ◽  
Dynamic Boundary ◽  
Linear Parabolic Equations

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.

scholarly journals Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Liming Xiao ◽  
Mingkun Li
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Evolution Problem ◽  
Positive Energy ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.

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