scholarly journals An isomorphism theorem for parabolic problems in Hörmander spaces and its applications

2017 ◽  
Vol 16 (1) ◽  
pp. 69-98 ◽  
Author(s):  
Valerii Los ◽  
◽  
Vladimir A. Mikhailets ◽  
Aleksandr A. Murach ◽  
◽  
...  
Keyword(s):  
Parabolic Problems ◽  
Isomorphism Theorem ◽  
Hörmander Spaces

scholarly journals Regularity of solutions to general parabolic problems in Hörmander spaces

2017 ◽  
pp. 3-10
Author(s):  
V.M. Los ◽  
◽  
V.A. Mikhailets ◽  
A.A. Murach ◽  
◽  
...  
Keyword(s):  
Regularity Of Solutions ◽  
Parabolic Problems ◽  
Hörmander Spaces

High-Order Finite Element Methods for Singularly-Perturbed Elliptic and Parabolic Problems.

1993 ◽  
Author(s):  
Slimane Adjerid ◽  
Mohammed Aiffa ◽  
Joseph E. Flaherty
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
High Order ◽  
Singularly Perturbed ◽  
Parabolic Problems

Protection Zones in Periodic-Parabolic Problems

2020 ◽  
Vol 20 (2) ◽  
pp. 253-276
Author(s):  
Julián López-Gómez
Keyword(s):  
Mixed Type ◽  
Principal Eigenvalue ◽  
Boundary Operator ◽  
General Boundary ◽  
Parabolic Problems ◽  
Parabolic Operator ◽  
Protection Zones ◽  
Competitive Environments

AbstractThis paper characterizes whether or not\Sigma_{\infty}\equiv\lim_{\lambda\uparrow\infty}\sigma[\mathcal{P}+\lambda m(% x,t),\mathfrak{B},Q_{T}]is finite, where {m\gneq 0} is T-periodic and {\sigma[\mathcal{P}+\lambda m(x,t),\mathfrak{B},Q_{T}]} stands for the principal eigenvalue of the parabolic operator {\mathcal{P}+\lambda m(x,t)} in {Q_{T}\equiv\Omega\times[0,T]} subject to a general boundary operator of mixed type, {\mathfrak{B}}, on {\partial\Omega\times[0,T]}. Then this result is applied to discuss the nature of the territorial refuges in periodic competitive environments.

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.

scholarly journals Regularity and time behavior of the solutions to weak monotone parabolic equations

2021 ◽  
Author(s):  
Maria Michaela Porzio
Keyword(s):  
Heat Equation ◽  
Parabolic Equations ◽  
Parabolic Problems ◽  
Summable Function ◽  
Time Behavior ◽  
Decay Estimates ◽  
Laplacian Equation ◽  
Evolution Problems ◽  
Degenerate Equations ◽  
Uniqueness Results

AbstractIn this paper, we study the behavior in time of the solutions for a class of parabolic problems including the p-Laplacian equation and the heat equation. Either the case of singular or degenerate equations is considered. The initial datum $$u_0$$ u 0 is a summable function and a reaction term f is present in the problem. We prove that, despite the lack of regularity of $$u_0$$ u 0 , immediate regularization of the solutions appears for data f sufficiently regular and we derive estimates that for zero data f become the known decay estimates for these kinds of problems. Besides, even if f is not regular, we show that it is possible to describe the behavior in time of a suitable class of solutions. Finally, we establish some uniqueness results for the solutions of these evolution problems.

scholarly journals INFINITARY PROPOSITIONAL RELEVANT LANGUAGES WITH ABSURDITY

2017 ◽  
Vol 10 (4) ◽  
pp. 663-681
Author(s):  
GUILLERMO BADIA
Keyword(s):  
Expressive Power ◽  
Interpolation Theorem ◽  
Boolean Logic ◽  
Isomorphism Theorem ◽  
Strong Completeness ◽  
Lack Of Compactness ◽  
Relevant Logics ◽  
Beth Definability ◽  
Beth Definability Property

AbstractAnalogues of Scott’s isomorphism theorem, Karp’s theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant logics. An “interpolation theorem” (of a particular sort introduced by Barwise and van Benthem) for the infinitary quantificational boolean logic L∞ω holds. This yields a preservation result characterizing the expressive power of infinitary relevant languages with absurdity using the model-theoretic relation of relevant directed bisimulation as well as a Beth definability property.

scholarly journals Analysis of a New Space-Time Parallel Multigrid Algorithm for Parabolic Problems

2016 ◽  
Vol 38 (4) ◽  
pp. A2173-A2208 ◽  
Author(s):  
Martin J. Gander ◽  
Martin Neumüller
Keyword(s):  
Space Time ◽  
Parabolic Problems ◽  
Multigrid Algorithm ◽  
New Space ◽  
Parallel Multigrid
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