Partial Differential Equations Research Group

Research output

Research output per year 2002 2014 2016 2018 2019 2020 2021 2022 2023 2023

• 178 Scopus Citations
• 7 h-index
• 47 Article
• 1 Conference contribution

Research output per year

Research output per year

Search results

• 2023

  Numerical analysis of a free boundary problem with non-local obstacles

  Li, Z. & Mikayelyan, H., Jan 2023, In: Applied Mathematics Letters. 135, 108414.

  Research output: Journal Publication › Article › peer-review

  • Comparison Principle 100%
  • Free Boundary Problem 95%
  • Numerical Analysis 84%
  • Numerical analysis 78%
  • Quasi-Newton Method 56%

• On the fractional Korn inequality in bounded domains: Counterexamples to the case ps < 1

  Harutyunyan, D. & Mikayelyan, H., 27 Feb 2023, In: Advances in Nonlinear Analysis. 12, 1, 20220283.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Korn's Inequality 100%
  • Counterexample 58%
  • Bounded Domain 54%
  • Fractional 49%
  • Hardy Inequality 20%
  1 Citation (Scopus)

• Orbital stability and concentration of standing-wave solutions to a nonlinear Schrodinger system with mass critical exponents

  Garrisi, D. & Gou, T., 1 Jan 2023, In: Nonlinear Differential Equations and Applications NoDEA. 30, p. 1-23 23 p., 3.

  Research output: Journal Publication › Article › peer-review

  • Orbital Stability 100%
  • Standing Wave 93%
  • Critical Exponents 82%
  • Minimizer 36%
  • Energy Functional 20%

• Positivity preserving truncated scheme for the stochastic Lotka–Volterra model with small moment convergence

  Cai, Y., Guo, Q. & Mao, X., 25 Apr 2023, In: Calcolo. 60, 24.

  Research output: Journal Publication › Article › peer-review

  • Lotka-Volterra Model 100%
  • Linearity 84%
  • Diffusion Coefficient 78%
  • Stochastic Model 75%
  • Positivity 73%
  3 Citations (Scopus)

• Stability and instability of standing-wave solutions to one-dimensional quadratic-cubic Klein–Gordon equations

  Garrisi, D., 4 Apr 2023, In: Journal of Fixed Point Theory and Applications. 25, 2, 19 p., 51.

  Research output: Journal Publication › Article › peer-review

  • Nonlinear Klein-Gordon Equation 100%
  • Cubic equation 94%
  • Standing Wave 92%
  • Klein-Gordon Equation 90%
  • Nonlinear equations 81%
• 2022

  Dynamics of adding variable prey refuge and an Allee effect to a predator–prey model

  Molla, H., Sarwardi, S., Smith?, S. R. & Haque, M., Jun 2022, In: AEJ - Alexandria Engineering Journal. 61, 6, p. 4175-4188 14 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Hopf bifurcation 100%
  • Bifurcation (mathematics) 91%
  • Dynamical systems 30%
  21 Citations (Scopus)

• High-Performance Adaptive Attitude Control of Spacecraft With Sliding Mode Disturbance Observer

  Javaid, U., Dong, H., Ijaz, S., Alkarkhi, T. & Haque, M., 2022, In: IEEE Access. 10, p. 41990-41999 10 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Attitude control 100%
  • Spacecraft 81%
  • Simulation 57%
  • Uncertainty 38%
  • System stability 31%
  5 Citations (Scopus)

• On some nonlocal problems in the calculus of variations

  Chipot, M. & Mikayelyan, H., Apr 2022, In: Nonlinear Analysis, Theory, Methods and Applications. 217, 112754.

  Research output: Journal Publication › Article › peer-review

  • Maximum principle 100%
  • Nonlocal Problems 87%
  • Calculus of variations 80%
  • Comparison Principle 42%
  • Maximum Principle 36%
  1 Citation (Scopus)

• Positivity and boundedness preserving numerical scheme for the stochastic epidemic model with square-root diffusion term

  Cai, Y., Hu, J. & Mao, X., Dec 2022, In: Applied Numerical Mathematics. 182, p. 100-116 17 p.

  Research output: Journal Publication › Article › peer-review

  • Stochastic Epidemic Models 100%
  • Stochastic models 79%
  • Square root 73%
  • Positivity 67%
  • Numerical Scheme 66%
  7 Citations (Scopus)
• 2021

  A stochastic differential equation SIS epidemic model with regime switching

  Cai, S., Cai, Y. & Mao, X., Sept 2021, In: Discrete and Continuous Dynamical Systems - Series B. 26, 9, p. 4887-4905 19 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • SIS Model 100%
  • Regime Switching 98%
  • Threshold Value 89%
  • Epidemic Model 78%
  • Differential equations 67%
  12 Citations (Scopus)

• Detecting the massive bosonic zero-mode in expanding cosmological spacetimes

  Toussaint, V. & Louko, J., 17 May 2021, In: Physical Review D. 103, 10, 105011.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • detectors 100%
  • scalars 86%
  • excitation 58%
  • sectors 52%
  • vacuum 37%
  4 Citations (Scopus)

• Erratum: Cylindrical optimal rearrangement problem leading to a new type obstacle problem (ESAIM - Control, Optimisation and Calculus of Variations (2018) 24 (859-872) DOI: 10.1051/cocv/2017047)

  Mikayelyan, H., 11 May 2021, In: ESAIM - Control, Optimisation and Calculus of Variations. 27, 41.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Obstacle Problem 100%
  • Rearrangement 94%
  • Calculus of variations 92%
  • Optimization 66%
  • Theorem 35%
  2 Citations (Scopus)

• Fractional optimal maximization problem and the unstable fractional obstacle problem

  Bonder, J. F., Cheng, Z. & Mikayelyan, H., 1 Mar 2021, In: Journal of Mathematical Analysis and Applications. 495, 1, 124686.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Obstacle Problem 100%
  • Rearrangement 94%
  • Laplace Operator 91%
  • Mathematical operators 80%
  • Unstable 72%
  1 Citation (Scopus)

• On the L^∞-maximization of the solution of Poisson's equation: Brezis-Gallouet-Wainger type inequalities and applications

  Harutyunyan, D. & Mikayelyan, H., Feb 2021, In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 151, 1, p. 79-92 14 p.

  Research output: Journal Publication › Article › peer-review

  • Poisson's equation 100%
  • Poisson Problem 41%
  • Norm 39%
  • L1-norm 38%
  • Modulus of Continuity 35%
  1 Citation (Scopus)

• Optimization problems and mathematical analysis of optimal values in orlicz spaces

  Donyari, Z., Zivari-Rezapour, M. & Emamizadeh, B., 2021, In: Electronic Journal of Differential Equations. 2021, 38.

  Research output: Journal Publication › Article › peer-review

  • Orlicz Spaces 100%
  • Mathematical Analysis 91%
  • Optimal Solution 77%
  • Optimization Problem 65%
  • Orlicz-Sobolev Spaces 62%
• 2020

  Analyticity of free boundary in an optimal harvesting problem

  Emamizadeh, B. & Liu, Y., 1 Jun 2020, In: Letters in Mathematical Physics. 110, 6, p. 1191-1199 9 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Optimal Harvesting 100%
  • free boundaries 86%
  • Analyticity 78%
  • Free Boundary 72%
  • Optimal Shape 50%
  42 Downloads (Pure)

• Bang-bang and multiple valued optimal solutions of control problems related to quasi-linear elliptic equations

  Emamizadeh, B. & Liu, Y., 2020, In: SIAM Journal on Control and Optimization. 58, 2, p. 1103-1117 15 p.

  Research output: Journal Publication › Article › peer-review

  • Admissible Set 100%
  • Quasilinear Elliptic Equation 87%
  • Control Problem 63%
  • Optimal Solution 63%
  • Set theory 48%
  2 Citations (Scopus)

• Existence of Continuous Eigenvalues for a Class of Parametric Problems Involving the (p, 2) -Laplacian Operator

  Bhattacharya, T., Emamizadeh, B. & Farjudian, A., 1 Feb 2020, In: Acta Applicandae Mathematicae. 165, 1, p. 65-79 15 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Boundary conditions 100%
  • Eigenvalue 82%
  • Principal Eigenvalue 80%
  • End point 72%
  • Half line 59%
  7 Citations (Scopus)

  41 Downloads (Pure)

• Multiple normalized standing-wave solutions to the scalar non-linear Klein-Gordon equation with two competing powers

  Garrisi, D., 15 Nov 2020, In: Journal of Differential Equations. 269, 11, p. 9189-9223 35 p.

  Research output: Journal Publication › Article › peer-review

  • Ground state 100%
  • Nonlinear Klein-Gordon Equation 87%
  • Standing Wave 81%
  • Scalar 50%
  • Ground State 47%
  1 Citation (Scopus)

• Optimal rearrangement problem and normalized obstacle problem in the fractional setting

  Bonder, J. F., Cheng, Z. & Mikayelyan, H., 1 Jan 2020, In: Advances in Nonlinear Analysis. 9, 1, p. 1592-1606 15 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Obstacle Problem 100%
  • Rearrangement 94%
  • Fractional 62%
  • Laplace Operator 45%
  • Minimization Problem 40%
  6 Citations (Scopus)

  37 Downloads (Pure)

• Overdetermined problems for p-Laplace and generalized Monge–Ampére equations

  Emamizadeh, B., Liu, Y. & Porru, G., 11 Nov 2020, In: Complex Variables and Elliptic Equations. 67, 4, p. 807-821 15 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Domain Derivative 100%
  • Overdetermined Problems 87%
  • Laplace 60%
  • Generalized Equation 59%
  • Derivatives 50%
  1 Citation (Scopus)

  44 Downloads (Pure)
• 2019

  Extension of Talenti’s Inequality and Maximum Values Relative to Rearrangement Classes

  Emamizadeh, B., Liu, Y. & Porru, G., 4 Apr 2019, In: Numerical Functional Analysis and Optimization. 40, 5, p. 586-602 17 p.

  Research output: Journal Publication › Article › peer-review

  • Rearrangement 100%
  • Poisson equation 59%
  • Class 27%
  • Admissible Set 24%
  • Sharpness 20%

• Extensions of a result by G. Talenti to (p,q)-Laplace equations

  Emamizadeh, B., Liu, Y. & Porru, G., Mar 2019, In: Nonlinear Analysis, Theory, Methods and Applications. 180, p. 41-51 11 p.

  Research output: Journal Publication › Article › peer-review

  • Laplace equation 100%
  • Comparison Result 85%
  • Laplace's equation 76%
  • P-Laplace Equation 49%
  • Symmetrization 44%
  3 Citations (Scopus)

• Maximum–norm a posteriori error estimates for an optimal control problem

  Otárola, E., Rankin, R. & Salgado, A. J., 1 Jul 2019, In: Computational Optimization and Applications. 73, 3, p. 997-1017 21 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Constrained Control 100%
  • A Posteriori Error Estimators 98%
  • A Posteriori Error Estimates 92%
  • Optimal Control Problem 66%
  • Rate of Convergence 63%
  2 Citations (Scopus)

  33 Downloads (Pure)

• Weighted asymptotic korn and interpolation korn inequalities with singular weights

  Harutyunyan, D. & Mikayelyan, H., 2019, In: Proceedings of the American Mathematical Society. 147, 8, p. 3635-3647 13 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Korn's Inequality 100%
  • Interpolation Inequality 96%
  • Interpolation 59%
  • Power rule 39%
  • Thin Domains 31%
  1 Citation (Scopus)
• 2018

  An a posteriori error analysis for an optimal control problem with point sources

  Allendes, A., Otárola, E., Rankin, R. & Salgado, A. J., 1 Sept 2018, In: ESAIM: Mathematical Modelling and Numerical Analysis. 52, 5, p. 1617-1650 34 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • A Posteriori Error Analysis 100%
  • Point Source 92%
  • A Posteriori Error Estimators 90%
  • Error analysis 70%
  • Optimal Control Problem 61%
  6 Citations (Scopus)

  29 Downloads (Pure)

• A posteriori error estimation for a PDE-constrained optimization problem involving the generalized oseen equations

  Allendes, A., Otarola, E. & Rankin, R., 2018, In: SIAM Journal of Scientific Computing. 40, 4, p. A2200-A2233

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • PDE-constrained Optimization 100%
  • Oseen Equations 97%
  • A Posteriori Error Estimation 86%
  • A Posteriori Error Estimators 80%
  • Constrained Optimization Problem 75%
  1 Citation (Scopus)

  39 Downloads (Pure)

• A posteriori error estimators for stabilized finite element approximations of an optimal control problem

  Allendes, A., Otárola, E. & Rankin, R., 1 Oct 2018, In: Computer Methods in Applied Mechanics and Engineering. 340, p. 147-177 31 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Stabilized Finite Elements 100%
  • optimal control 87%
  • A Posteriori Error Estimators 83%
  • estimators 76%
  • Finite Element Approximation 70%
  2 Citations (Scopus)

• A unified analysis of algebraic flux correction schemes for convection–diffusion equations

  Barrenechea, G. R., John, V., Knobloch, P. & Rankin, R., Dec 2018, In: SeMA Journal. 75, 4, p. 655-685 31 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Convection-diffusion Equation 100%
  • Fluxes 72%
  • Limiters 36%
  • Limiter 29%
  • Numerical analysis 25%
  32 Citations (Scopus)

• Cylindrical optimal rearrangement problem leading to a new type obstacle problem

  Mikayelyan, H., 1 Apr 2018, In: ESAIM - Control, Optimisation and Calculus of Variations. 24, 2, p. 859-872 14 p.

  Research output: Journal Publication › Article › peer-review

  • Obstacle Problem 100%
  • Rearrangement 94%
  • Derivatives 71%
  • Comparison Principle 48%
  • Minimizer 41%
  4 Citations (Scopus)

• Optimal harvesting strategy based on rearrangements of functions

  Emamizadeh, B., Farjudian, A. & Liu, Y., 1 Mar 2018, In: Applied Mathematics and Computation. 320, p. 677-690 14 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Optimal Harvesting 100%
  • Harvesting 86%
  • Rearrangement 78%
  • Boats 57%
  • Strategy 51%
  7 Citations (Scopus)

  34 Downloads (Pure)

• Stationarity of the crack-front for the Mumford–Shah problem in 3D

  Lemenant, A. & Mikayelyan, H., 15 Jun 2018, In: Journal of Mathematical Analysis and Applications. 462, 2, p. 1555-1569 15 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Stationarity 100%
  • Stationary Solutions 93%
  • Crack 89%
  • Minimizer 88%
  • Mumford-Shah Functional 71%
• 2017

  An Elliptic Optimal Control Problem and its Two Relaxations

  Emamizadeh, B., Farjudian, A. & Mikayelyan, H., 1 Feb 2017, In: Journal of Optimization Theory and Applications. 172, 2, p. 455-465 11 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Free Boundary 100%
  • Numerical Algorithms 94%
  • Control Theory 91%
  • Optimal Control Problem 81%
  • Shape optimization 70%
  1 Citation (Scopus)

  27 Downloads (Pure)

• Converse symmetry and intermediate energy values in rearrangement optimization problems

  Liu, Y. & Emamizadeh, B., 2017, In: SIAM Journal on Control and Optimization. 55, 3, p. 2088-2107 20 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Rearrangement 100%
  • Converse 85%
  • Optimization Problem 66%
  • Energy Functional 65%
  • Symmetry 63%
  7 Citations (Scopus)

  28 Downloads (Pure)

• Stabilization technique applied to curve shortening flow in the plane

  Mikayelyan, H., Jul 2017, In: Journal of Mathematical Sciences. 224, 3, p. 442-447 6 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Monotonicity Formula 100%
  • Mean Curvature Flow 87%
  • Stars 74%
  • Star 65%
  • Stabilization 63%
  1 Citation (Scopus)
• 2016

  Existence and uniqueness of solutions for nonlocal p-Laplacian problems

  Emamizadeh, B. & Farjudian, A., 12 Oct 2016, In: Electronic Journal of Differential Equations. 2016, 274.

  Research output: Journal Publication › Article › peer-review

  • Sobolev Embedding 100%
  • P-Laplacian Operator 93%
  • Nonlocal Boundary Value Problems 91%
  • P-Laplacian 76%
  • Existence and Uniqueness of Solutions 72%

• Fine numerical analysis of the crack-tip position for a Mumford-Shah minimizer

  Li, Z. & Mikayelyan, H., 2016, In: Interfaces and Free Boundaries. 18, 1, p. 75-90 16 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  • Crack Tip 100%
  • free boundaries 91%
  • Free Discontinuity Problems 83%
  • crack tips 82%
  • Crack tips 77%

• Optimization problems with fixed volume constraints and stability results related to rearrangement classes

  Liu, Y., Emamizadeh, B. & Farjudian, A., 15 Nov 2016, In: Journal of Mathematical Analysis and Applications. 443, 2, p. 1293-1310 18 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Rearrangement 100%
  • Optimization Problem 66%
  • Trace Inequality 41%
  • Admissible Set 40%
  • Converge 38%
  4 Citations (Scopus)

  31 Downloads (Pure)

• Optimization related to some nonlocal problems of Kirchhoff type

  Emamizadeh, B., Farjudian, A. & Zivari-Rezapour, M., Jun 2016, In: Canadian Journal of Mathematics. 68, 3, p. 521-540 20 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Nonlocal Problems 100%
  • Rearrangement 93%
  • Optimization 65%
  • Free Boundary Problem 60%
  • Minimization Problem 54%
  2 Citations (Scopus)

  32 Downloads (Pure)

• Rearrangement minimization problems with indefinite external forces

  Liu, Y. & Emamizadeh, B., 1 Nov 2016, In: Nonlinear Analysis, Theory, Methods and Applications. 145, p. 162-175 14 p.

  Research output: Journal Publication › Article › peer-review

  • Admissible Set 100%
  • Rearrangement 81%
  • Minimization Problem 70%
  • Boundary value problems 55%
  • Optimal Solution 47%
  6 Citations (Scopus)
• 2015

  Absolute continuity in partial differential equations

  Farjudian, A. & Emamizadeh, B., 1 Jan 2015, In: Real Analysis Exchange. 40, 1, p. 209-218

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Absolute Continuity 100%
  • Partial differential equation 60%
  • Definite integral 52%
  • Hamilton-Jacobi 49%
  • Absolutely Continuous 41%
  26 Downloads (Pure)

• Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator

  Emamizadeh, B. & Liu, Y., Feb 2015, In: Israel Journal of Mathematics. 206, 1, p. 281-298 18 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • P-Laplace Operator 100%
  • Constrained Minimization 90%
  • Rearrangement 80%
  • Energy Functional 78%
  • Minimization Problem 69%
  16 Citations (Scopus)

  40 Downloads (Pure)
• 2014

  Maximal mean exit time related to the p-Laplace operator

  Farjudian, A. & Emamizadeh, B., 2014, In: Applied Mathematics E - Notes. 14, p. 173-184 12 p.

  Research output: Journal Publication › Article › peer-review

  • P-Laplace Operator 100%
  • Exit Time 95%
  • Boundary value problems 82%
  • Mathematical operators 68%
  • Boundary Value Problem 51%

• Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string

  Emamizadeh, B. & Farjudian, A., 15 Aug 2014, In: Nonautonomous Dynamical Systems. 1, 1, p. 123-136 14 p.

  Research output: Journal Publication › Article › peer-review

  Open Access

  File

  • Principal Eigenvalue 100%
  • Monotonicity 68%
  • Strings 67%
  • Rearrangement 43%
  • Numerical Algorithms 39%
  1 Citation (Scopus)

  32 Downloads (Pure)

• Rearrangement optimization problems with free boundary

  Emamizadeh, B. & Marras, M., 3 Apr 2014, In: Numerical Functional Analysis and Optimization. 35, 4, p. 404-422 19 p.

  Research output: Journal Publication › Article › peer-review

  • Rearrangement 100%
  • Free Boundary 91%
  • Optimization Problem 66%
  • Area formula 35%
  • Poisson Boundary 34%
  5 Citations (Scopus)

• Some results on radial symmetry in partial differential equations

  Farjudian, A. & Emamizadeh, B., 2014, In: New York Journal of Mathematics. 20, p. 241-255 15 p.

  Research output: Journal Publication › Article › peer-review

  • Radial Symmetry 100%
  • Optimal Domain 56%
  • Partial differential equation 54%
  • Ball 44%
  • Domain Derivative 30%
  2 Citations (Scopus)
• 2002

  Asymptotic summation of operator-valued Volterra symbols

  Mikayelyan, H., 2002, In: Journal of Contemporary Mathematical Analysis. 37, 3, p. 76-80 5 p.

  Research output: Journal Publication › Article › peer-review