Results 211 to 220 of about 87,102,086 (248)

Second-order linear elliptic PDEs: weak solutions

CMS/CAIMS Books in Mathematics, 2023
exaly   +2 more sources

Weak solutions to the Cauchy problem of fractional time‐space Keller–Segel equation

Mathematical methods in the applied sciences, 2021
This paper investigates the Cauchy problem of the time‐space fractional parabolic‐elliptic Keller–Segel equation in ℝd,d≥2 . The global existence and mass conservation of weak solutions are established.
Zi‐wen Jiang, Li-Zhen Wang
semanticscholar   +1 more source

Global weak solutions in a three-dimensional two-species cancer invasion haptotaxis model without cell proliferation

Journal of Mathematics and Physics, 2022
This paper considers the two species cancer invasion haptotaxis model without cell proliferation in three space dimensions. The system consists of two parabolic partial differential equations (PDEs) describing the migration of differentiated cancer cells
Feng Dai, Bin Liu
semanticscholar   +1 more source

Optimization Problems for PDEs in Weak Space-Time Form

Oberwolfach Reports, 2023
Optimization problems constrained by time-dependent Partial Differential Equations (PDEs) are challenging from a computational point of view: even in the simplest case, one needs to solve a system of PDEs coupled globally in time and space for the ...
H. Harbrecht, A. Kunoth, Valeria Simoncini, Karsten Urban   +3 more
semanticscholar   +1 more source

Existence and Uniqueness of Bounded Weak Solutions of a Semilinear Parabolic PDE

Journal of Theoretical Probability, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ran, Qikang, Zhang, Tusheng
openaire   +1 more source

PRINCIPLE OF STRUCTURAL ANALOGY OF SOLUTIONS AND ITS APPLICATION TO NONLINEAR PDEs AND DELAY PDEs [PDF]

Journal of Mathematical Sciences
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related equations. It
Andrei Polyanin
exaly   +2 more sources

Existence and multiplicity of weak solutions for a system of fourth‐order elliptic equations with combined nonlocal and indefinite source terms

Mathematical methods in the applied sciences
This manuscript aims to investigate the existence of weak solutions for a system of partial differential equations (PDEs) described by Equation (1.2). The system consists of a set of PDEs with Leray–Lions operators and nonlinear terms.
K. Kefi
semanticscholar   +1 more source

A note on transforming a weak solution to PDE to a smooth solution

International Journal of Financial Engineering, 2016
This is paper, we develop a simple method that transforms weak solutions to PDEs to smooth solutions. We apply our method to the portfolio model.
openaire   +1 more source

A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances

MCSS. Mathematics of Control, Signals and Systems, 2019
In this paper, we introduce a weak maximum principle-based approach to input-to-state stability (ISS) analysis for certain nonlinear partial differential equations (PDEs) with certain boundary disturbances.
Jun Zheng, Guchuan Zhu
semanticscholar   +1 more source

On the differentiability of weak solutions of a degenerate system of PDE's in fluid mechanics

Annali di Matematica Pura ed Applicata, 1988
Weak solutions, in problems of fluid mechanics, are generalized solutions usually constructed in order to describe the behaviour of phenomena such as discontinuities, for example. In the present paper, the author studies the differentiability of weak solutions for a nonnewtonian fluid (here, a pseudo-plastic fluid). Namely, the author derives a theorem
openaire   +1 more source