is well posed

USAGE SUMMARY

The phrase "is well posed" is correct and usable in written English.
It is typically used in contexts such as mathematics or philosophy to indicate that a problem or question is clearly defined and has a solution. Example: "The mathematical problem is well posed, allowing for a straightforward approach to finding the solution."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

28 human-written examples

Thus the following definition is well posed.

Bulletin of Mathematical Sciences

Then the fixed point equation (27) is well posed.

Fixed Point Theory and Applications

However, the problem is well posed as mentioned above.

Boundary Value Problems

end{aligned} such that (u_{0}) is well posed.

Journal of Inequalities and Applications

The problem is well posed for any (alpha > 0).

Boundary Value Problems

Therefore, the fixed point problem is well posed.

Fixed Point Theory and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

32 human-written examples

Thus, (OPLEC) is well-posed.

Journal of Inequalities and Applications

Then (LVQEPLEC) is well-posed at (bar{lambda}).

Journal of Inequalities and Applications

Thus, (LVQEPLEC) is well-posed at (bar{lambda}).

Journal of Inequalities and Applications

Consequently, (OPLEC) is well-posed at (bar{lambda}).

Journal of Inequalities and Applications

Then (OPLEC) is well-posed at (bar{lambda}).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "is well posed" in technical writing, ensure that you have clearly defined all terms and conditions relevant to the problem or equation. This helps maintain clarity and avoids ambiguity for your audience.

Common error

Avoid using "is well posed" too broadly. This term specifically refers to problems that have a unique solution, depend continuously on the initial data, and have clearly defined conditions. Applying it loosely can mislead readers.

Linguistic Context

The phrase "is well posed" functions as an adjectival phrase, specifically used to describe a problem, equation, or system that meets certain criteria for having a valid and stable solution. Ludwig confirms its grammatical correctness and typical usage in technical fields.

Expression frequency: Common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

The phrase "is well posed" is a technical term primarily used in scientific and mathematical contexts to describe problems that are properly defined and have stable, unique solutions. Ludwig AI confirms that this phrase is grammatically correct and frequently appears in academic and scientific literature. When using this phrase, ensure all terms are clearly defined to avoid ambiguity. Alternative phrases include "is clearly defined" or "is properly formulated". The consistent use and authoritative sources underscore its importance in technical writing and analysis.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

is clearly defined

This alternative focuses on the clarity and unambiguity of the problem or definition.

is properly formulated

This alternative emphasizes the correct and appropriate structuring of the problem.

is rigorously defined

This alternative highlights the strictness and precision of the definition.

is validly constructed

This phrase stresses the soundness and logical correctness of the construction.

is soundly established

This emphasizes the firm and reliable foundation upon which something is based.

is appropriately framed

This alternative highlights how a problem is presented and set up.

is correctly specified

This alternative stresses the accuracy and detail in the specification of a problem or system.

is unambiguously stated

This focuses on the lack of ambiguity and the directness of the statement.

is logically consistent

This alternative highlights that the elements of a problem or definition do not contradict each other.

is admissibly defined

This implies that the definition conforms to certain acceptable standards or rules.

FAQs

How is "is well posed" typically used in mathematical contexts?

In mathematics, "is well posed" describes a problem that has a unique solution, depends continuously on the initial data, and satisfies certain conditions. Ensuring a problem "is well posed" is crucial for reliable and predictable outcomes.

What does it mean for a problem to be "is well posed"?

When a problem "is well posed", it means that a solution exists, that the solution is unique, and that the solution's behavior changes continuously with the initial conditions. This concept is important in fields like mathematics, physics, and engineering.

Which fields commonly use the term "is well posed"?

The term "is well posed" is frequently used in fields such as mathematics, physics, engineering, and computer science to describe problems that satisfy certain conditions for solvability and stability. For example, a differential equation "is well posed" if its solution exists, is unique, and is stable with respect to changes in initial conditions.

What are some alternatives to saying a problem "is well posed"?

Depending on the specific context, you can use alternatives like "is clearly defined", "is properly formulated", or "is rigorously defined" to convey that a problem meets certain criteria for solvability and stability.