Backward uniqueness results for some parabolic equations in an infinite rod

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.

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Uniqueness of renormalized solutions to nonlinear parabolic problems with lower-order terms

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210511001831 ◽

2013 ◽

Vol 143 (6) ◽

pp. 1185-1208 ◽

Cited By ~ 6

Author(s):

Rosaria Di Nardo ◽

Filomena Feo ◽

Olivier Guibé

Keyword(s):

Parabolic Equations ◽

Dirichlet Boundary ◽

Growth Conditions ◽

Dirichlet Boundary Conditions ◽

Parabolic Problems ◽

Renormalized Solutions ◽

Uniqueness Results ◽

Nonlinear Parabolic ◽

Image Position ◽

Lower Order Terms

We consider a general class of parabolic equations of the typewith Dirichlet boundary conditions and with a right-hand side belonging to L1 + Lp′ (W−1, p′). Using the framework of renormalized solutions we prove uniqueness results under appropriate growth conditions and Lipschitz-type conditions on a(u, ∇u), K(u) and H(∇u).

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Existence and uniqueness results for parabolic equations with Robin type boundary conditions in a non-regular domain of R3

Applied Mathematics and Computation ◽

10.1016/j.amc.2013.07.027 ◽

2013 ◽

Vol 220 ◽

pp. 756-769 ◽

Cited By ~ 4

Author(s):

Arezki Kheloufi

Keyword(s):

Boundary Conditions ◽

Parabolic Equations ◽

Existence And Uniqueness ◽

Regular Domain ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Type Boundary

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Backward Uniqueness for Parabolic Equations

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-003-0263-8 ◽

2003 ◽

Vol 169 (2) ◽

pp. 147-157 ◽

Cited By ~ 103

Author(s):

L. Escauriaza ◽

G. Seregin ◽

V. Šverák

Keyword(s):

Parabolic Equations ◽

Backward Uniqueness

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On nonclassical problems for first-order evolution equations

Georgian Mathematical Journal ◽

10.1515/gmj.2011.0028 ◽

2011 ◽

Vol 18 (3) ◽

pp. 441-463

Author(s):

Gia Avalishvili ◽

Mariam Avalishvili

Keyword(s):

Boundary Value Problems ◽

Parabolic Equations ◽

Evolution Equations ◽

Initial Conditions ◽

Boundary Value ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

First Order ◽

Uniqueness Results ◽

Initial Boundary Value

Abstract The present paper deals with nonclassical initial-boundary value problems for parabolic equations and systems and their generalizations in abstract spaces. Nonclassical problems with nonlocal initial conditions for an abstract first-order evolution equation with time-dependent operator are considered, the existence and uniqueness results are proved and the algorithm of approximation of nonlocal problems by a sequence of classical problems is constructed. Applications of the obtained general results to initial-boundary value problems for parabolic equations and systems are considered.

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

Filomat ◽

10.2298/fil1704057s ◽

2017 ◽

Vol 31 (4) ◽

pp. 1057-1064 ◽

Cited By ~ 6

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.

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