Initial Boundary Value Problem for Partial Differential–Algebraic Equations With Parameter
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DOI: 10.1002/mma.10663
Abstract: The paper addresses an initial boundary value problem for a partial differential–algebraic equation involving a parameter. An integral condition with respect to the time derivative of the unknown function is provided as an additional condition… read more here.
Keywords: problem; boundary value; value problem; initial boundary ... See more keywords
Semigroup Dynamics and Chaotic Behavior in Second‐Order Partial Differential Equations on H1×L2 Space
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DOI: 10.1002/mma.10675
Abstract: This paper focuses on the dynamics of a second‐order partial differential equation within the space L2$$ {L}^2 $$ described by ∂2ϑ(x,t)∂t2+a∂ϑ(x,t)∂t+bϑ(x,t)=c∂2ϑ(x,t)∂x2+h(x,t),a,b,c>0.$$ \frac{\partial^2\vartheta \left(x,t\right)}{\partial {t}^2}+a\frac{\partial \vartheta \left(x,t\right)}{\partial t}+ b\vartheta \left(x,t\right)=c\frac{\partial^2\vartheta \left(x,t\right)}{\partial {x}^2}+h\left(x,t\right),a,b,c>0. $$ Under suitable conditions… read more here.
Keywords: order partial; space; partial vartheta; left right ... See more keywords
Semilinear stochastic partial differential equations: Central limit theorem and moderate deviations
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DOI: 10.1002/mma.7224
Abstract: In this paper, we establish a central limit theorem (CLT) and the moderate deviation principles (MDP) for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main… read more here.
Keywords: partial differential; semilinear stochastic; central limit; stochastic partial ... See more keywords
Crack Propagation Prediction Using Partial Differential Equations‐Based Neural Network With Discovered Governing Equations
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DOI: 10.1002/nme.7665
Abstract: This paper presents a regularization technique using discovered partial differential equations (PDEs) with an example of a surrogate model of crack propagation. Regularization techniques are so essential in machine learning to improve generalization performance. Recently,… read more here.
Keywords: crack propagation; differential equations; propagation; loss ... See more keywords
Summability of Formal Solutions for Some Generalized Moment Partial Differential Equations
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DOI: 10.1007/s00025-020-01324-y
Abstract: The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment… read more here.
Keywords: moment; partial differential; formal solutions; summability formal ... See more keywords
On Some Stochastic Hyperbolic Equations with Symplectic Characteristics
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DOI: 10.1007/s00041-025-10159-6
Abstract: We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions. The coefficients of our partial differential operators contain harmonic oscillators in… read more here.
Keywords: equations symplectic; symplectic characteristics; hyperbolic equations; stochastic hyperbolic ... See more keywords
Maillet type theorem for nonlinear totally characteristic partial differential equations
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DOI: 10.1007/s00208-019-01864-x
Abstract: The paper discusses a holomorphic nonlinear singular partial differential equation $$(t \partial _t)^mu=F(t,x,\{(t \partial _t)^j \partial _x^{\alpha }u \}_{j+\alpha \le m, j read more here.
Keywords: nonlinear totally; maillet type; partial differential; totally characteristic ... See more keywords
A simple algorithm for numerical solution of nonlinear parabolic partial differential equations
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DOI: 10.1007/s00366-019-00796-z
Abstract: In this paper, numerical solution of nonlinear two-dimensional parabolic partial differential equations with initial and Dirichlet boundary conditions is considered. The time derivative is approximated using finite difference scheme whereas space derivatives are approximated using… read more here.
Keywords: partial differential; numerical solution; solution nonlinear; method ... See more keywords
Maurice Janet’s algorithms on systems of linear partial differential equations
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DOI: 10.1007/s00407-020-00255-y
Abstract: This article describes the emergence of formal methods in theory of partial differential equations (PDE) in the French school of mathematics through Janet’s work in the period 1913–1930. In his thesis and in a series… read more here.
Keywords: partial differential; algorithms systems; janet algorithms; differential equations ... See more keywords
A gaussian process framework for solving forward and inverse problems involving nonlinear partial differential equations
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DOI: 10.1007/s00466-024-02559-0
Abstract: Physics-informed machine learning (PIML) has emerged as a promising alternative to conventional numerical methods for solving partial differential equations (PDEs). PIML models are increasingly built via deep neural networks (NNs) whose architecture and training process… read more here.
Keywords: gaussian process; differential equations; partial differential; process framework ... See more keywords
Gaussian process for estimating parameters of partial differential equations and its application to the Richards equation
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DOI: 10.1007/s00477-019-01709-8
Abstract: This paper proposes a new collocation method for estimating parameters of a partial differential equation (PDE), which uses Gaussian process (GP) as a basis function and is termed as Gaussian process for partial differential equation… read more here.
Keywords: partial differential; estimating parameters; method; equation ... See more keywords