Symmetry groups and fundamental solutions for systems of parabolic equations

2012 ◽  
Vol 53 (2) ◽  
pp. 023509 ◽  
Author(s):  
Jing Kang ◽  
Changzheng Qu
Keyword(s):  
Parabolic Equations ◽  
Fundamental Solutions ◽  
Symmetry Groups ◽  
Systems Of Parabolic Equations

Stability in 𝐿𝑞-norm for inverse source parabolic problems

2020 ◽  
Vol 28 (6) ◽  
pp. 797-814
Author(s):  
Elena-Alexandra Melnig
Keyword(s):  
Parabolic Equations ◽  
Main Tool ◽  
Parabolic Systems ◽  
Carleman Estimates ◽  
Parabolic Problems ◽  
Lebesgue Spaces ◽  
First Order ◽  
Lipschitz Estimates ◽  
Systems Of Parabolic Equations

AbstractWe consider systems of parabolic equations coupled in zero and first order terms. We establish Lipschitz estimates in {L^{q}}-norms, {2\leq q\leq\infty}, for the source in terms of the solution in a subdomain. The main tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for nonhomogeneous parabolic systems.

Controllability of Semilinear Systems of Parabolic Equations with Delay on the State

2015 ◽  
Vol 17 (6) ◽  
pp. 2105-2114 ◽  
Author(s):  
A. Carrasco ◽  
Hugo Leiva ◽  
N. Merentes ◽  
J. L. Sanchez
Keyword(s):  
Parabolic Equations ◽  
The State ◽  
Semilinear Systems ◽  
Systems Of Parabolic Equations ◽  
Equations With Delay

scholarly journals Oscillation of the solutions of systems of nonlinear parabolic equations with functional arguments

2007 ◽  
Vol 38 (4) ◽  
pp. 367-379
Author(s):  
Yutaka Shoukaku
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Differential Inequalities ◽  
Dimensional Problem ◽  
Limit Condition ◽  
Nonlinear Functional ◽  
One Dimensional ◽  
Nonlinear Parabolic ◽  
Functional Differential ◽  
Systems Of Parabolic Equations

In the present paper the oscillatory properties of the solutions of systems of parabolic equations are investigated and oscillation criteria is derived for every solution of boundary value problems to be oscillatory or satisfies some limit condition. Our approach is to reduce the multi-dimensional problem to a one-dimensional problem for nonlinear functional differential inequalities.

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