Results 1 to 10 of about 802 (148)

Existence of Weak Solutions to Nonlocal PDEs With a Generalized Definition of Caputo Derivative

Mediterranean Journal of Mathematics, 2023
Some compactness criteria that are analogies of the Aubin–Lions lemma for the existence of weak solutions of nonlinear evolutionary PDEs play crucial roles for the existence of weak solutions to time-fractional PDEs. Based on this fact, in this paper, we consider the existence of weak solutions to a kind of partial differential equations with Caputo ...
Xu, Jiaohui, Caraballo Garrido, Tomás
openaire   +3 more sources

Can There Be a General Nonlinear PDE Theory for Existence of Solutions? [PDF]

Reviews in Theoretical Science, 2015
Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the ...
openaire   +2 more sources

Classic Solutions of Boundary Value Problems for Partial Differential Equations with Operator of Finite Index in the Main Part of Equation

Известия Иркутского государственного университета: Серия "Математика", 2019
This paper is an attempt to give the review of a part of our results in the area of singular partial differential equations. Using the results of the theory of complete generalized Jordan sets we consider the reduction of the PDE with the irreversible ...
N.A. Sidorov
doaj   +1 more source

On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients

Journal of Applied Mathematics, 2013
We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values.
A. De Cezaro
doaj   +1 more source

Logarithmic capacity and Riemann and Hilbert problems for generalized analytic functions

Доповiдi Нацiональної академiї наук України
The study of the Dirichlet problem with arbitrary measurable boundary data for harmonic functions in the unit disk is due to the famous Luzin dissertation.
V.Ya. Gutlyanskiĭ, O.V. Nesmelova, V.I. Ryazanov, A.S. Yefimushkin   +3 more
doaj   +1 more source

Can there be a general nonlinear PDE theory for the existence of solutions ?

, 2004
Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the ...
openaire   +2 more sources

Implicit quiescent soliton perturbation in optical metamaterials with complex Ginzburg-Landau equation having nonlinear chromatic dispersion and Kudryashov's forms of self-phase modulation structures by lie symmetry. [PDF]

MethodsX
Adem AR, Arnous AH, Triki H, González-Gaxiola O, Calucag LS, Biswas A.   +5 more
europepmc   +1 more source

Understanding the impacts of extreme weather on biological control through traveling wave analysis of a prey-predator model. [PDF]

Sci Rep
Aktar MS, Yue Y, Bani-Yaghoub M, Ou C, Ali MA.   +4 more
europepmc   +1 more source

Exploration of nonclassical symmetries and exact solutions to the (4+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. [PDF]

Sci Rep
Ur Rahman M, Akram S, Asif M.
europepmc   +1 more source

Steady-State and Dynamical Behavior of a PDE Model of Multilevel Selection with Pairwise Group-Level Competition. [PDF]

Bull Math Biol
Alexiou K, Cooney DB.
europepmc   +1 more source