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Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions
This paper is devoted to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. First, we prove the...
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Approximation of an Inverse Initial Problem for a Biparabolic Equation
In this paper, we consider the problem of finding the initial distribution for the linear inhomogeneous and nonlinear biparabolic equation. The...
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Modified B-Spline Collocation Approach for Pricing American Style Asian Options
In this work, a stable numerical scheme based on modified bi-cubic B-spline collocation method is developed for the valuation of Asian options. The...
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Continuity of Solutions of a Class of Fractional Equations
In practice many problems related to space/time fractional equations depend on fractional parameters. But these fractional parameters are not known a...
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The modified simple equation method and the multiple exp-function method for solving nonlinear fractional Sharma-Tasso-Olver equation
In this article, the fractional derivatives in the sense of the modified Riemann-Liouville derivatives together with the modified simple equation...
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On the Exponential Convergence Rate for a Non-Gradient Fokker-Planck Equation in Computational Neuroscience
This paper concerns the proof of the exponential rate of convergence of the solution of a Fokker-Planck equation, with a drift term not being the...
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On a general filter regularization method for the 2D and 3D Poisson equation in physical geodesy
In this paper, we consider a Cauchy problem for the Poisson equation with nonhomogeneous source. The problem is shown to be ill-posed as the solution...
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Exact solutions of Kolmogorov-Petrovskii-Piskunov equation using the modified simple equation method
The modified simple equation method is employed to find the exact solutions of the nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation. When...
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On an initial inverse problem in nonlinear heat equation associated with time-dependent coefficient
In this paper, a nonlinear backward heat problem with time-dependent coefficient in the unbounded domain is investigated. A modified regularization...
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Determination temperature of a backward heat equation with time-dependent coefficients
We introduce the truncation method for solving a backward heat conduction problem with time-dependent coefficients. For this method, we give the...
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An ALE ESFEM for Solving PDEs on Evolving Surfaces
Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite elements on...
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Regional gradient observability for distributed semilinear parabolic systems
In this paper, we extend the notion of regional observability of the gradient for linear systems to a class of semilinear parabolic systems. To...
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Phase-field Approaches to Structural Topology Optimization
The mean compliance minimization in structural topology optimization is solved with the help of a phase field approach. Two steepest descent...
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Anomalous Diffusion: Models, Their Analysis, and Interpretation
In this chapter, modeling of anomalous diffusion processes in terms of differential equations of an arbitrary (not necessarily integer)ord er is...
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Fractional-Parabolic Systems
We develop a theory of the Cauchy problem for linear evolution systems of partial differential equations with the Caputo-Dzhrbashyan fractional...
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Maximum principle and its application for the time-fractional diffusion equations
In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion...
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On using the modified variational iteration method for solving the nonlinear coupled equations in the mathematical physics
This paper applied the modified variational iteration method to the nonlinear coupled partial differential equations via the generalized nonlinear...
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Closure Properties of Solutions to Heat Inequalities
We prove that if u 1 , u 2 :(0,∞)×ℝ d →(0,∞) are sufficiently well-behaved solutions to certain heat inequalities on ℝ d then the function u :(0,∞)×ℝ ...
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The ( \(\frac{G'}{G})\) -expansion method and its applications to some nonlinear evolution equations in the mathematical physics
In the present paper, we construct the traveling wave solutions involving parameters for some nonlinear evolution equations in the mathematical...