scholarly journals Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions

2011 ◽  
Vol 31 ◽  
pp. 73-100
Author(s):  
Gerardo Rubio
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Semilinear Parabolic Equations ◽  
Local Conditions ◽  
The Cauchy Problem ◽  
Semilinear Parabolic

Existence and uniqueness results for an inverse problem for semilinear parabolic equations

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1057-1064 ◽  
Author(s):  
Ali Sazaklioglu ◽  
Allaberen Ashyralyev ◽  
Abdullah Erdogan
Keyword(s):  
Inverse Problem ◽  
Difference Scheme ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Semilinear Parabolic Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Accuracy Difference ◽  
Integral Overdetermination ◽  
Semilinear Parabolic

In the present study, unique solvability of an inverse problem governed by semilinear parabolic equations with an integral overdetermination is investigated. Furthermore, for the approximate solution of this problem a first order of accuracy difference scheme is constructed. Existence and uniqueness results for the solution of this difference scheme are established. Considering a particular example, some numerical results are discussed.

scholarly journals The Cauchy Problem for Parabolic Equations with Degeneration

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Ivan Pukal’skii ◽  
Bohdan Yashan
Keyword(s):  
Boundary Condition ◽  
Cauchy Problem ◽  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Arbitrary Order ◽  
Power Weight ◽  
The Cauchy Problem ◽  
Uniqueness Of The Solution ◽  
Set Of Points

Annotation. For a second-order parabolic equation, the multipoint in time Cauchy problem is considered. The coefficients of the equation and the boundary condition have power singularities of arbitrary order in time and space variables on a certain set of points. Conditions for the existence and uniqueness of the solution of the problem in Hölder spaces with power weight are found.

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