On some boundary-value problems with a shift on characteristics for a mixed equation of hyperbolic-parabolic type

2000 ◽  
Vol 52 (5) ◽  
pp. 809-820 ◽  
Author(s):  
V. A. Eleev ◽  
S. K. Kumykova
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Parabolic Type ◽  
Mixed Equation

scholarly journals Boundary value problems of elliptic and parabolic type with boundary data of negative regularity

2021 ◽  
Author(s):  
Felix Hummel
Keyword(s):  
Boundary Value Problems ◽  
Half Space ◽  
Boundary Data ◽  
Boundary Value ◽  
Parabolic Type ◽  
Normal Direction ◽  
Parabolic Boundary ◽  
Parabolic Boundary Value Problems ◽  
Mixed Smoothness

AbstractWe study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half-space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the singularities of solutions at the boundary. To this end, we derive mapping properties of Poisson operators in mixed scales with mixed smoothness. We also derive $$\mathcal {R}$$ R -sectoriality results for homogeneous boundary data in the case that the smoothness in normal direction is not too large.

Non-well-ordered lower and upper solutions for semilinear systems of PDEs

2021 ◽  
pp. 2150080
Author(s):  
Alessandro Fonda ◽  
Giuliano Klun ◽  
Andrea Sfecci
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Parabolic Type ◽  
Existence Results ◽  
Second Order ◽  
Lower And Upper Solutions ◽  
Semilinear Systems ◽  
Systems Of Pdes ◽  
Abstract Framework

We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.

scholarly journals On Boundary Value Problems for a Mixed Type Fractional Differential Equation with Caputo Operator

2021 ◽  
Vol 101 (1) ◽  
pp. 127-137
Author(s):  
T.K. Yuldashev ◽  
◽  
B.I. Islomov ◽  
U.Sh. Ubaydullaev ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Fourier Series ◽  
Boundary Value Problems ◽  
Unique Solvability ◽  
Mixed Type ◽  
Boundary Value ◽  
Rectangular Domain ◽  
Hyperbolic Type ◽  
Mixed Equation ◽  
Fractional Differential

This article is devoted to study the boundary value problems of the first and second kind with respect to the spatial variable for a mixed inhomogeneous differential equation of parabolic-hyperbolic type with a fractional Caputo operator in a rectangular domain. In the study of such boundary value problems, we abandoned the boundary value condition with respect to the first argument and instead it is used additional gluing condition. In this case, in the justification of the unique solvability of the problems, the conditions on the boundary domain are removed. This allowed us to weaken the criterion for the unique solvability of boundary value problems under consideration. The solution is constructed in the form of Fourier series with eigenfunctions corresponding to homogeneous spectral problems. Estimates for the convergence of Fourier series are obtained as a regular solution of this mixed equation.

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