Abstract
In the paper, similarity solutions are constructed for a model equation with multiple characteristics of an arbitrary integer order. It is shown that the structure of similarity solutions depends on the mutual simplicity of the orders of derivatives with respect to the variable x and y, respectively. Frequent cases are considered in which they are shown as fundamental solutions of well-known equations, expressed in a linear way through the constructed similarity solutions.
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Articles in the same Issue
- Frontmatter
- A pair of rational double sequences
- On a new method of the testing hypothesis of equality of two Bernoulli regression functions for group observations
- Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
- A Robin boundary value problem for the Cauchy–Riemann operator in a ring domain
- Particular solutions of equations with multiple characteristics expressed through hypergeometric functions
- One remark on the inverse scattering problem for the perturbed Stark operator on the semiaxis
- On a geometric statement of Ramsey type
- Positive answer to the invariant and hyperinvariant subspaces problems for hyponormal operators
- Approximation on a new class of Szász–Mirakjan operators and their extensions in Kantorovich and Durrmeyer variants with applicable properties
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- Absolute convergence factors of Lipschitz class functions for general Fourier series
Articles in the same Issue
- Frontmatter
- A pair of rational double sequences
- On a new method of the testing hypothesis of equality of two Bernoulli regression functions for group observations
- Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
- A Robin boundary value problem for the Cauchy–Riemann operator in a ring domain
- Particular solutions of equations with multiple characteristics expressed through hypergeometric functions
- One remark on the inverse scattering problem for the perturbed Stark operator on the semiaxis
- On a geometric statement of Ramsey type
- Positive answer to the invariant and hyperinvariant subspaces problems for hyponormal operators
- Approximation on a new class of Szász–Mirakjan operators and their extensions in Kantorovich and Durrmeyer variants with applicable properties
- Regularity properties of nonlocal fractional differential equations and applications
- Solutions of a singular integro-differential equation related to the adhesive contact problems of elasticity theory
- Positive periodic solutions to the forced non-autonomous Duffing equations
- Absolute convergence factors of Lipschitz class functions for general Fourier series