On finite products of convolutions and classifications of hyperbolic and elliptic equations. by Kilicman, Adem, Eltayeb, Hassan

“…In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new equations. …”
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On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models by Archie J. Huang, Shaurya Agarwal

“…Since its introduction in 2017, physics-informed deep learning (PIDL) has garnered growing popularity in understanding the systems governed by physical laws in terms of partial differential equations (PDEs). However, empirical evidence points to the limitations of PIDL for learning certain types of PDEs. …”
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On a characteristic problem for a loaded hyperbolic equation by A.Kh. Attaev

“…The above verifies once more the thesis of load influencing on posing of various initial - boundary value problem for partial differential equations. …”
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An approximation to the solution of hyperbolic equation by homotopy analysis method by Ismail, Siti Hajar

“…In this research, Homotopy Analysis Method (HAM) is a analytical method that be used to obtained the approximation solution of hyperbolic equation. Hyperbolic equation is a one of the class of Partial Differential Equation (PDE). …”
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TRAVELING WAVE SOLUTIONS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS by SERIFE MUGE EGE, EMINE MISIRLI

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Dynamics Behavior of Lumps and Interaction Solutions of a (3+1)-Dimensional Partial Differential Equation by Bo Ren

“…In this work, we investigate a linear partial differential equation in (3+1)-dimensions. …”
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Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay by Tomasz Człapiński

“…We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. …”
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New Exact Solutions of Some Important Nonlinear Fractional Partial Differential Equations with Beta Derivative by Erdogan Mehmet Ozkan

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Mechanical Solving a Few Fractional Partial Differential Equations and Discussing the Effects of the Fractional Order by Kai Fan, Cunlong Zhou

“…The solutions of fractional-order nonlinear partial differential equations can be enriched by selecting other solvable equations as auxiliary equations.…”
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Almost automorphic mild solutions of hyperbolic evolution equations with stepanov-like almost automorphic forcing term by Indira Mishra, Dhirendra Bahuguna

“…This article concerns the existence and uniqueness of almost automorphic solutions to the semilinear parabolic boundary differential equations $$displaylines{ x'(t)=A_mx(t)+f(t,x(t)), quad tin mathbb{R}, cr Lx(t)=phi(t,x(t)), quad tin mathbb{R}, }$$ where $A:=A_m|_{ker L}$ generates a hyperbolic analytic semigroup on a Banach space $X$, with Stepanov-like almost automorphic nonlinear term, defined on some extrapolated space $X_{alpha-1}$, for $0<alpha<1$ and $phi$ takes values in the boundary space $partial X$.…”
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Novel Analytical Technique to Find Closed Form Solutions of Time Fractional Partial Differential Equations by Muhammad Shakeel, Nehad Ali Shah, Jae Dong Chung

“…In this article, a new method for obtaining closed-form solutions of the simplified modified Camassa-Holm (MCH) equation, a nonlinear fractional partial differential equation, is suggested. …”
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A guide to the design of the virtual element methods for second- and fourth-order partial differential equations by Yu Leng, Lampros Svolos, Dibyendu Adak, Ismael Boureima, Gianmarco Manzini, Hashem Mourad, Jeeyeon Plohr

“…The two partial differential equations are: (i) a linear hyperbolic equation describing the momentum balance and (ii) a fourth-order elliptic equation modeling the damage of the material. …”
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Significant Production of Thermal Energy in Partially Ionized Hyperbolic Tangent Material Based on Ternary Hybrid Nanomaterials by Umar Nazir, Muhammad Sohail, Muhammad Bilal Hafeez, Marek Krawczuk

“…To reduce the complexity, the derived PDEs (partial differential equations) were transformed into a set of ordinary differential equations (ODEs) by engaging in similarity transformations. …”
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Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations by Olivier Sarbach, Manuel Tiglio

“…The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein's equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.…”
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Hyperbolic Gradient-Bourgoignon Flow by Hamed Faraji, Shahroud Azami, Ghodratallah Fasihi-Ramandi

“…This ‎flow ‎is a‎ ‎system ‎of ‎non-linear ‎evolution ‎partial ‎differential ‎equation‎s of second order. ‎…”
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Polynomial differential systems with hyperbolic algebraic limit cycles by Salah Benyoucef

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Existence and asymptotic behavior of solutions for Henon equations in hyperbolic spaces by Haiyang He, Wei Wang

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Stability of the time-dependent identification problem for delay hyperbolic equations by A. Ashyralyev, B. Haso

“… Time-dependent and space-dependent source identification problems for partial differential and difference equations take an important place in applied sciences and engineering, and have been studied by several authors. …”
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Stability of the time-dependent identification problem for delay hyperbolic equations by A. Ashyralyev, B. Haso

“… Time-dependent and space-dependent source identification problems for partial differential and difference equations take an important place in applied sciences and engineering, and have been studied by several authors. …”
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Morawetz’s contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed type by Chen, G-QG

“…This article is a survey of Cathleen Morawetz’s contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed elliptic-hyperbolic type. …”