Very Weak Solutions to the Boundary-Value Problem of the Homogeneous Heat Equation

2013 ◽  
Vol 32 (2) ◽  
pp. 129-153 ◽  
Author(s):  
Bernard Nowakowski ◽  
Woiciech Zajączkowski
Keyword(s):  
Boundary Value Problem ◽  
Heat Equation ◽  
Weak Solutions ◽  
Boundary Value ◽  
Very Weak Solutions

scholarly journals Integrability of Very Weak Solutions for Boundary Value Problems of Nonhomogeneous p-Harmonic Equations

2019 ◽  
pp. 1-9
Author(s):  
Yeqing Zhu ◽  
Yanxia Zhou ◽  
Yuxia Tong
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Weak Solutions ◽  
Boundary Value ◽  
Very Weak Solutions ◽  
Very Weak Solution ◽  
Harmonic Equation

The paper deals with very weak solutions u to boundary value problems of the nonhomogeneous p-harmonic equation. We show that, any very weak solution u to the boundary value problem is integrable provided that r is sufficiently close to p.

EXISTENCE AND UNIQUENESS OF WEAK AND CLASSICAL SOLUTIONS FOR A FOURTH-ORDER SEMILINEAR BOUNDARY VALUE PROBLEM

2019 ◽  
Vol 61 (3) ◽  
pp. 305-319
Author(s):  
CRISTIAN-PAUL DANET
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Classical Solutions ◽  
Maximum Principles ◽  
Uniqueness Results

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles.

scholarly journals Entropy Solution for Doubly Nonlinear Elliptic Anisotropic Problems with Robin Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
I. Ibrango ◽  
S. Ouaro
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Weak Solutions ◽  
Entropy Solution ◽  
Boundary Value ◽  
Monotone Operators ◽  
Robin Boundary Conditions ◽  
Anisotropic Problems ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

We study in this paper nonlinear anisotropic problems with Robin boundary conditions. We prove, by using the technic of monotone operators in Banach spaces, the existence of a sequence of weak solutions of approximation problems associated with the anisotropic Robin boundary value problem. For the existence and uniqueness of entropy solutions, we prove that the sequence of weak solutions converges to a measurable function which is the entropy solution of the anisotropic Robin boundary value problem.

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