degenerate equations
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Author(s):  
Maria Michaela Porzio

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.


2020 ◽  
Vol 72 (4) ◽  
pp. 495-514
Author(s):  
T. Gadjiev ◽  
M. Kerimova ◽  
G. Gasanova

2020 ◽  
Vol 194 ◽  
pp. 111332
Author(s):  
Luís H. de Miranda ◽  
Adilson E. Presoto
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2020 ◽  
Vol 72 (4) ◽  
pp. 435-451
Author(s):  
T. Gadjiev ◽  
M. Kerimova ◽  
G. Gasanova

UDC 517.9 We consider a boundary-value problem for degenerate equations with discontinuous coefficients and establish the unique strong solvability (almost everywhere) of this problem in the corresponding weighted Sobolev space.


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